Answer:
27 dollars
Step-by-step explanation:
On one side he had 175
One the other side he has 6 books and 13 dollars
175 = 6b+13
Subtract 13 from each side
175 -13 = 6b+13-13
162 = 6b
Divide each side by 6
162/6 = 6b/6
27 = b
Each book is 27 dollars
A baby weighs 81/4 pound's at birth two weeks later she weighs 87/8 pounds how much weight did the baby gain
Answer:75/8
Step-by-step explanation:
weight gain=81/4-87/8
weight gain=(2x81-1x87)/8
Weight gain=(162-87)/8
weight gain =75/8
in a sample of people on the school board, 2 out of 5 were in favor of a new high school being built. If 3,500 people vote in the next local election approximately how many would vote against the new high school being built?
Answer:
2,100 people.
Step-by-step explanation:
If 2 out of 5 people were in favor of a new high school being built, we know that 3 out of 5 people are against the decision. We can simply use this as a fraction to find the amount of people against:
[tex]3500 * \frac{3}{5}= 2100[/tex]
Therefore, 2,100 people are against the decision.
A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they conclude that more than 60 percent of the city residents support the proposal. A survey of 2,000 randomly selected city residents will be conducted to investigate the level of support for the proposal. Let X represent the number of city residents in the sample who support the proposal. Assume that X is a binomial random variable.
Determine the mean and the standard deviation of the random variable X, assuming that 60 percent of city henudng proosal to create a new city park.
Answer:
The mean of the the random variable X is 1200.
The standard deviation of the random variable X is 21.91.
Step-by-step explanation:
The random variable X is defined as the number of city residents in the sample who support the proposal.
The random variable X follows a Binomial distribution with parameters n = 2000 and p = 0.60.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10Check the conditions as follows:
[tex]np=2000\times 0.60=1200>10\\\\n(1-p)=2000\times (1-0.60)=800>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, the random variable X can be approximate by the Normal distribution .
Compute the mean of X as follows:
[tex]\mu=np[/tex]
[tex]=2000\times 0.60\\=1200[/tex]
The mean of the the random variable X is 1200.
Compute the standard deviation of X as follows:
[tex]\sigma=\sqrt{np(1-p)}[/tex]
[tex]=\sqrt{2000\times 0.60\times (1-0.60)}\\=\sqrt{480}\\=21.9089\\\approx 21.91[/tex]
The standard deviation of the random variable X is 21.91.
In 1929 Edwin Hubble investigated the claim that distance (explanatory) and radial velocity (response) of extragalactic nebulae are positively linearly related. Hubble's data is plotted below along with the relevant diagnostic plots. These are the plots and charts needed to analyze data are given below. (Assume all observations are independent) Reference: Hubble, E. (1929) "A Relationship Between Distance and Radial Velocity among Extra-Galactic Nebulae," Proceedings of the National Academy of Science, 168.The explanatory variable is distance (in megaparsecs) and the response is radial velocity (velocity away or towards the earth). Use 3 decimal places for the following questions.(a) What is the regression equation?(b) What is the estimated mean velocity of objects that are 1.9 megaparsecs from Earth?(c) If you were to test the claim that there is a positive linear relationship between the explanatory and response variable, what would your null and alternative hypotheses be?H0: a = 0 and Ha: a < 0H0: a = 0 and Ha: a ? 0 H0: a = 0 and Ha: a > 0H0: b = 0 and Ha: b < 0H0: b = 0 and Ha: b ? 0H0: b = 0 and Ha: b > 0
Answer:
honestly this is very confusing could you send a graph?
Step-by-step explanation:
Explore the area of sectors of circles by following these steps.
1. What is the area of circle
Check
Answer: 9pi
Step-by-step explanation:
Describe how to determine which of two negative numbers is greater.
Give an example,
Answer:
on the no. line the negative no.s are to the left of zero. -5 is less than 4 because -5 lies to the left of 4 on the no. line -1 is greater than -3 because -1 lies to the right of -3 on the no. line . for less than you can use the sign <- sign
Step-by-step explanation:
-2>-9
7x^2 > -2x^2
6 > -8
pls mark me brainliest if you feel this answer helps you.
if you have any question pls feel to ask in the comment section.
thanks.
How does using a check register help you manage money?
Answer:
Inside a checkbook is the register. This is where you record events in your checking account such as checks you've written, cash withdrawals, and deposits. It's very important to write down every transaction so you know exactly how much money you have in the bank.
Step-by-step explanation:
Answer:
You can store your money in an organized fashion, separating them by type (penny, dime, $1, $5, etc.).
If a sunspot has a temperature of 3900 K and the photosphere of the Sun has a temperature of 5760 K, how many times
brighter per unit area is the photosphere than the sunspot?
The photosphere is approximately 5.62 times brighter per unit area than the sunspot.
Stefan-Boltzmann Law: We'll use the Stefan-Boltzmann Law, which states that the radiant emittance (power emitted per unit area) of a black body is proportional to the fourth power of its absolute temperature (T). Mathematically, this can be expressed as:
M = σ * T^4
Where:
M is the radiant emittance (W/m²)
σ is the Stefan-Boltzmann constant (5.670374 x 10^-8 W m^-2 K^-4)
T is the absolute temperature (Kelvin)
Radiant Emittance: Calculate the radiant emittance of the sunspot and the photosphere using their respective temperatures:
Sunspot: M_sunspot = σ * T_sunspot^4 = 5.670374e-8 * 3900^4 ≈ 83.32 x 10^12 W/m²
Photosphere: M_photosphere = σ * T_photosphere^4 = 5.670374e-8 * 5760^4 ≈ 468.37 x 10^12 W/m²
Brightness Ratio: Calculate the ratio of the photosphere's radiant emittance to the sunspot's radiant emittance to determine how much brighter the photosphere is per unit area:
Brightness Ratio = M_photosphere / M_sunspot ≈ 468.37 x 10^12 W/m² / 83.32 x 10^12 W/m² ≈ 5.62
Therefore, the photosphere is approximately 5.62 times brighter per unit area than the sunspot.
brody and amanda canoed 1 1/2 hours before stopping to fish at 11:15 pm. at what time did amanda start canoeing.
Answer:
9:45 pm
Step-by-step explanation:
1 1/2 hours is 1 hour 30 min
11:15 - 1 hr 30 = 9:45
Answer:
9:45 im pretty sure :)
Step-by-step explanation:
So they canoed for 1 hour and 30 minutes. so you subtract 1:30 from 11:15
What is the perimeter of the square that has the same area as the rectangle?
18 ft
5 ft
A) 9.49 ft
OB) 23 ft
OC) 37.96 ft
OD) 90 ft
Answer:
A) 9.49 ft
Step-by-step explanation:
The area of the rectangle is:
[tex]A = (18\,ft)\cdot (5\,ft)[/tex]
[tex]A = 90\,ft^{2}[/tex]
The length of the square is:
[tex]l = \sqrt{90\,ft^{2}}[/tex]
[tex]l \approx 9.487\,ft[/tex]
Is y=33x proportional or non proportional
Answer:
proportional
Step-by-step explanation:
Determine the measure of the arc length of the following segment of a circle.
97°
11
a. 10.67
b. 0.47
c. 18.6
d. 37.2
Answer:
c is correct
Step-by-step explanation:
edge
the arc length of the following segment of a circle is c. 18.6.
What is arc length?Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.
here, we have,
given that,
the following segment of a circle.
angle=97°
radius=11
so, the arc length= 18.6
hence, the arc length of the following segment of a circle is c. 18.6.
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Leona has a bag containing letter tiles. Which describes dependent events?
Answer:
a) removing a vowel, not replacing it, and then removing another vowel
Step-by-step explanation:
This question is from the topic Probability. In Probability, a dependent event is one in which the outcome of one event alters or changes the outcome of another event. A classic example of this is seen when sampling without replacement is done. When sampling without replacement is done, the outcome of another event within the same set changes. When sampling with replacement is done, the outcome of the events are independent because every item in the population still has an equal chance of being chosen. However, in the case of sampling without replacement, once an item has been selected from a population, the outcome of every other event after it is altered based on the item that was initially chosen.
Let's assume that the bag has 26 tiles (one for each alphabet from a - z)
Population = 26, consonant = 21, vowel = 5
If a vowel or consonant is removed & is replaced, we have:
Pr (choosing "a") = number of item ÷ population
Pr = 1 ÷ 26 = 1/26
Pr (choosing "y") = 1 ÷ 26 = 1/26
Doing this for over & over again, produces the same probability
However, if an item was selected without replacement, we have:
Pr (choosing "a") = 1 ÷ 26 = 1/26
Without replacement implies that if I choose tile letter "a", tile letter "a" will not be included in subsequent events, hence:
Population = 25
Pr (choosing "u") = 1 ÷ 25 = 1/25
Without replacement, population = 24
Pr (choosing "y") = 1 ÷ 24 = 1/24
So, we see the dependent nature of the events in how that the outcome of the next event is being altered. As such, option a describes a dependent event & is the correct answer
Answer:
A. removing a vowel, not replacing it, and then removing another vowel
simple answer ^^
Step-by-step explanation:
EDGE 2021 : )
A conservative investor desires to invest in a bond fund in which her investment amount is kept relatively safe. A national investment group claims to have a bond fund which has maintained a consistent share price of $11.25, consistent because the variation in price (as measured by standard deviation) is at most $0.45 since fund inception. To test this claim, the investor randomly selects fifty days during the last year and determines the share price for the fund on closing of those days. The standard deviation of this sample group is found to be $0.62. Use an appropriate hypothesis test at the 5% significance level to determine if the investor should conclude that the variation is greater than that claimed by the national investment group.
Give the null and alternative hypotheses for this test in symbolic form.
Answer:
[tex]\chi^2 =\frac{50-1}{0.2025} 0.3844 =93.015[/tex]
The degrees of freedom are given by:
[tex] df = n-1= 50-1=49[/tex]
And the p value is given by:
[tex]p_v =P(\chi^2 >93.015)=0.00015[/tex]
Since the p value is very low compared to the significance level provided we have enough evidence to conclude that the true deviation is higher than 0.45
Step-by-step explanation:
Information given
[tex]\alpha=0.05[/tex] represent the confidence level
[tex]s^2 =0.62^2 =0.3844 [/tex] represent the sample variance obtained
[tex]\sigma^2_0 =0.45^2 =0.2025[/tex] represent the value that we want to test
System of hypothesis
On this case we want to check if the true deviation is higher than 0.45, so then we can create the following system of hypothesis:
Null Hypothesis: [tex]\sigma^2 \leq 0.2025[/tex]
Alternative hypothesis: [tex]\sigma^2 >0.2025[/tex]
The statistic for this case is given by:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
Replacing we got
[tex]\chi^2 =\frac{50-1}{0.2025} 0.3844 =93.015[/tex]
The degrees of freedom are given by:
[tex] df = n-1= 50-1=49[/tex]
And the p value is given by:
[tex]p_v =P(\chi^2 >93.015)=0.00015[/tex]
Since the p value is very low compared to the significance level provided we have enough evidence to conclude that the true deviation is higher than 0.45
Gauges are used to reject all components for which a certain dimension is not within the specification 1.5 d . It is known that this measurement is normally distributed with mean 1.5 and standard deviation 0.2. Determine the value d such that the specifications cover 95% of the measurements.
The value of 'd' such that the specifications cover 95% of the measurements can be determined using the z-score corresponding to a 95% confidence interval, and is found to be 0.392 by multiplying with the known standard deviation.
Explanation:In this case, you're looking to find the value for d such that specifications cover 95% of the measurements. We know that the measurements follow a normal distribution, with a mean of 1.5 and a standard deviation of 0.2.
According to the Empirical Rule (for a bell-shaped, symmetric distribution), approximately 95 percent of the data is within two standard deviations of the mean. Here, however, we want to find the distance d from the mean that encapsulates 95% of the data. We already know that d falls within a 95% confidence interval, which splits the excluded 5% evenly between the upper and lower tails of the distribution.
So, we will use a z-score corresponding to 95% of the measurements. The z-score corresponding to 95% is approximately 1.96 (covering 2.5% in each tail). Multiply this z-score by the standard deviation to get the value of d (1.96 * 0.2 = 0.392). Thus, d = 0.392 should be the value that ensures the specifications cover 95% of the measurements.
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A survey asked, "How many tattoos do you currently have on your body?" Of the 1230 males surveyed, 176 responded that they had at least one tattoo. Of the 1079 females surveyed, 141 responded that they had at least one tattoo. Construct a 95% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.
Answer:
The 95% confidence interval for p₁-p₂
( -0.01564 ,0.04044 )
Step-by-step explanation:
Explanation:-
Given data Of the 1230 males surveyed, 176 responded that they had at least one tattoo
Given the first sample size 'n₁' = 1230
Given x = 176
The first sample proportion
[tex]p_{1} = \frac{x}{n_{1} } = \frac{176}{1230} =0.1430[/tex]
q₁ = 1-p₁ =1-0.1430 = 0.857
Given data Of the 1079 females surveyed, 141 responded that they had at least one tattoo
Given the second sample size n₂ = 1079
and x = 141
The second sample proportion
[tex]p_{2} = \frac{x}{n_{2} } = \frac{141}{1079} = 0.1306[/tex]
q₂ = 1-p₂ = 1-0.1306 =0.8694
The 95% confidence interval for p₁-p₂
[tex](p_{1} - p_{2} - Z_{\frac{\alpha }{2} } se(p_{1} - p_{2}) ,p_{1} - p_{2} + Z_{\frac{\alpha }{2} } se(p_{1} - p_{2})[/tex]
where
[tex]se(p_{1}-p_{2}) = \sqrt{\frac{p_{1}q_{1} }{n_{1} }+\frac{p_{2} q_{2} }{n_{2} } }[/tex]
[tex]se(p_{1}-p_{2}) = \sqrt{\frac{0.143(0.857) }{1230}+\frac{ 0.1306(0.8694) }{1079 }[/tex]
se(p₁-p₂) = 0.01431
[tex](p_{1} - p_{2} - Z_{\frac{\alpha }{2} } se(p_{1} - p_{2}) ,p_{1} - p_{2} + Z_{\frac{\alpha }{2} } se(p_{1} - p_{2})[/tex]
[tex][(0.1430-0.1306) - 1.96(0.01431) , 0.1430-0.1306) + 1.96(0.01431)[/tex]
On calculation , we get
( 0.0124- 0.0280476 ,0.0124+ 0.0280476)
( -0.01564 ,0.04044 )
Conclusion:-
The 95% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.
( -0.01564 ,0.04044 )
What is the sample space for the random phenomenon flip a coin three times?
The U-Drive Rent-A-Truck company plans to spend $14 million on 280 new vehicles. Each commercial van will cost $55 comma 000, each small truck $20 comma 000, and each large truck $70 comma 000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? They can buy nothing vans, nothing small trucks, and nothing large trucks.
Answer: They can buy 140 vans, 70 small trucks, and 70 large trucks.
Step-by-step explanation:
Let x represent the cost of each commercial van.
Let y represent the cost of each small truck.
Let z represent the cost of each large truck.
The total number if vehicles that they want to purchase is 280. It means that
x + y + z = 280- - - - - - - - - - - 1
Each commercial van will cost $55 000, each small truck $20000, and each large truck $70000. The total amount to be spent is $14000000. It means that
55000x + 20000y + 70000z = 14000000- - - - - - -2
Past experience shows that they need twice as many vans as small trucks. It means that
x = 2y
Substituting x = 2y into equation 1 and equation 2, it becomes
2y + y + z = 280
3y + z = 280
z = 280 - 3y - - - - - - - - -3
55000(2y) + 20000y + 70000z = 14000000
110000y + 20000y + 70000z = 14000000
130000y + 70000z = 14000000- - - - - - - 4
Substituting equation 3 into equation 4, it becomes
130000y + 70000(280 - 3y) = 14000000
130000y + 19600000 - 210000y = 14000000
130000y - 210000y = 14000000 - 19600000
- 80000y = -5600000
y = -5600000/- 80000
y = 70
x = 2y = 2 × 70
x = 140
z = 280 - 3y = 280 - 3(70)
z = 280 - 210
z = 70
An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet. What is the volume of the tank? Use 3.14 for Pi. A cylinder has a height of 50 feet and diameter of 20 feet. 15,700 cubic feet 39,250 cubic feet 62,800 cubic feet 78,500 cubic feet
Answer:
15,700 cubic feet
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
where r is the radius (half the diameter), and h is the height.
Put the given numbers into the formula and do the arithmetic.
V = (3.14)(10 ft)²(50 ft) = 15,700 ft³
__
An estimate of the arithmetic will get you to the right answer choice:
πr²h = π(100)(50) = 5000π ≈ 3×5000 = 15,000 . . . . close to 15,700
Answer:
15,700 cubic feet
Step-by-step explanation:
Need help on these two!!
Answer:
The first one is false and the second is vertex
Step-by-step explanation:
You have decided to set a new goal of saving at least $4,500 over the
course of the next year.
You already have $900 saved.
By how much would you need to increase your monthly net savings in
order to meet this goal?
$100
$150
$200
$250
Answer: $200
Step-by-step explanation:
Answer:
The answer is C.
Ryan has 3 cups of chocolate milk. If he pours 1/3 of a cup each day, how many days will the 3 cups last him?
9514 1404 393
Answer:
9 days
Step-by-step explanation:
Divide quantity by rate to find time.
(3 cups)(1/3 cup/day) = 3/(1/3) days = 3(3/1) days = 9 days
how to subtract fractons with unlike denominators
Answer:
so first you cross multiply the first fractions' numerator by the other fractions denominator.
and then you do the same for the other one
then you multiply both denominators
the answer u got from cross multiplying, you get those numbers and subtract
them. the denominator doesn't need anything done to it.
Step-by-step explanation:
hope it helps (pls brainliest if u can)
I need help on the rounding tto try to get the right answer. Maybe mark branliest?
Answer:
3238.37571429
Step-by-step explanation:
or 3238.4
Find the value of x
REVIEW
The point (4, 3) is rotated 90o clockwise about the origin. What are the coordinates of the resulting point?
A. (-3, 4)
B. (-4, 3)
C. (4, -3)
D. (3, -4)
Answer:
D. (3, -4)
Step-by-step explanation:
Imagine you are going 4 right and 3 up.
Now if you turn this 90o clockwise, you are going 4 down and 3 right.
that is (3, -4)
Final answer:
Rotating the point (4, 3) 90 degrees clockwise about the origin results in the point (3, -4), making option D the correct answer.
Explanation:
The question asks about rotating the point (4, 3) 90 degrees clockwise about the origin and determining the coordinates of the resulting point. To rotate a point 90 degrees clockwise around the origin, you can switch the x and y coordinates and then change the sign of the new y-coordinate. Thus, the original point (4, 3) becomes (3, -4) after the rotation.
This process can be visualized as a transformation where the point's x-coordinate effectively becomes the y-coordinate but negative, and the y-coordinate becomes the new x-coordinate. This transformation corresponds to choice D. (3, -4) as the correct answer. This method is a straightforward application of rotation in the coordinate system, relying on the rules of rotating points in two-dimensional space.
Lily goes car shopping and finds two cars. The first one burns fossil fuel, gasoline, that sells for $18,000. It will cost $100 each month to buy fuel and maintain this car. The second car is a fuel cell car that is cleaner for the environment, but costs $22,400. It will cost $60 each month to run and maintain this car.
If Lilly keeps the car for 5 years, how much will each car cost to buy and run over the 5 year period? Which car should Lilly buy?
Answer:
Cost to buy and run the first car for 5 years=$24000
Cost to buy and run the second car for 5 years=$26000
I think we should buy the first car, because It is cheaper to buy and maintain
Step-by-step explanation:
first car:
Cost $18000 to buy
Cost $100 to maintain each month
5years =5 x 12=60months
Cost to maintain for 60months=100x60=$6000
First car cost to buy and run over the 5 year period=18000+6000=$24000
Second car:
It cost $22400 to buy
Cost $60 to maintain each month
5years=60months
Cost to maintain for 60months is 60 x 60=$3600
Cost to buy and run over the second car for 5years is 22400+3600=$26000
A random sample of 10 shipments of stick-on labels showed the following order sizes. 22,485 56,758 59,762 17,671 16,301 12,262 48,307 51,196 47,326 31,943 Click here for the Excel Data File (a) Construct a 95 percent confidence interval for the true mean order size. (Round your standard deviation answer to 1 decimal place and t-value to 3 decimal places. Round your answers to the nearest whole number.) The 95 percent confidence interval to (b) The confidence interval can be made narrower by: increasing the sample size or decreasing the confidence level. increasing the sample size or increasing the confidence level. decreasing the sample size or decreasing the confidence level. decreasing the sample size or increasing the confidence level.
Answer:
a) [tex]36401.1-2.262\frac{18230.58}{\sqrt{10}}=23360.63 \approx 23361[/tex]
[tex]36401.1+2.262\frac{18230.58}{\sqrt{10}}=49441.56 \approx 49442[/tex]
b) increasing the sample size or decreasing the confidence level
Since if we increase the sample size the margin of error would be lower and if we decrease the confidence level the margin of error would be reduced since the critical value t would be lower
Step-by-step explanation:
We have the following data given
22,485 56,758 59,762 17,671 16,301 12,262 48,307 51,196 47,326 31,943
We can calculate the sample mean and deviation with this formula:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=36401.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s= 18230.58 represent the sample standard deviation
n=10 represent the sample size
Part a
The confidence interval for the mean is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The Confidence level is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]t_{\alpha/2}=2.262[/tex]
Replacing the info given we got:
[tex]36401.1-2.262\frac{18230.58}{\sqrt{10}}=23360.63 \approx 23361[/tex]
[tex]36401.1+2.262\frac{18230.58}{\sqrt{10}}=49441.56 \approx 49442[/tex]
Part b
The confidence interval can be made narrower:
increasing the sample size or decreasing the confidence level
Since if we increase the sample size the margin of error would be lower and if we decrease the confidence level the margin of error would be reduced since the critical value t would be lower
What is 5.3809 rounded to the nearest thousandth?
Enter your answer
The answer is 5.381!
The number 5.3809 rounded to the nearest thousandth is 5.381 because the thousandth is 3 decimals.
What is rounding off number?Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.
We have a number:
= 5.3809
The thousandth(3 decimals) place is:
Rounded to the nearest 0.001 or the Thousandths Place.
The number becomes:
= 5.381
Thus, the number 5.3809 rounded to the nearest thousandth is 5.381 because the thousandth is 3 decimals.
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One year, the mean age of an inmate on death row was 39.2 years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 37.6, with a standard deviation of 9.89.8. Construct a 95% confidence interval about the mean age. What does the interval imply?
Answer:
The 95% confidence interval about the mean age is between 17.6 years and 57.6 years.
This means that we are 95% sure that the mean age of an inmate in the death row is in this interval. 39.2 is part of this interval, which implies that the mean age of a death-row inmate has not changed since then.
Step-by-step explanation:
We have the sample standard deviation, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 32 - 1 = 31
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 31 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0395
The margin of error is:
M = T*s = 2.0395*9.8 = 20
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 37.6 - 20 = 17.6 years
The upper end of the interval is the sample mean added to M. So it is 37.6 + 20 = 57.6 years.
The 95% confidence interval about the mean age is between 17.6 years and 57.6 years.
This means that we are 95% sure that the mean age of an inmate in the death row is in this interval. 39.2 is part of this interval, which implies that the mean age of a death-row inmate has not changed since then.
Final answer:
To construct a 95% confidence interval about the mean age of death-row inmates, we can use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size). In this case, the 95% confidence interval is approximately 35.8 to 39.4 years old.
Explanation:
To construct a 95% confidence interval about the mean age, we can use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).
In this case, the sample mean is 37.6, the standard deviation is 9.8, and the sample size is 32. To find the critical value, we look up the z-score for a 95% confidence level, which is approximately 1.96.
Substituting these values into the formula, we have:
37.6 ± 1.96 * (9.8 / √32)
Simplifying the equation gives us the 95% confidence interval of approximately 35.8 to 39.4. This means that we are 95% confident that the true mean age of death-row inmates falls within this interval.