It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and found no evidence to reject the null hypothesis at the 5% significance level. What is true regarding the p-value from this hypothesis test?
Answer:
Given:
Sample size, n = 20
Significance level = 5% = 0.05
Mean, u = 8
Here, the sample mean was not given.
Here the null and alternative hypothesis will be:
H0 : u = 8
H1 : u < 8
In this case, since there is no evidence to reject the null hypothesis, H0, at 0.05 level of significance, we can say that the p-value is greater than the level of significance, 0.05.
Which statement(s) could describe the graph of a nonproportional relationship? Select all that apply
Answer:
A. The positive y-intercept.
D. The y-intercept is negative.
Step-by-step explanation:
The proportional relationship is defined by the graph passing through the origin i.e. the y-intercept is equal to zero.
The equation of y proportional to x relationship is y = kx, which again denotes that the graph passes through the origin (0,0).
Now, the statements that can describe the graph of a non-proportional relationship are
A. The positive y-intercept.
D. The y-intercept is negative. (Answer)
The statements that could describe the graph of a nonproportional relationship include:
A. The positive y-intercept.D. The y-intercept is negative.It should be noted that the proportional relationship is defined by the graph passing through the origin. The equation of y proportional to x relationship is y = kx.
From the information given, the relationship shows that the positive y-intercept and the y-intercept is negative.
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Timothy creates a game in which the player rolls 4 dice. What is the probability in this game of having exactly two dice or more land on a five?
A. 0.016
B. 0.132
C. 0.868
D. 0.984
Answer:
B. 0.132
Step-by-step explanation:
For each time the dice is thrown, there are only two possible outcomes. Either it lands on a five, or it does not. The probability of a throw landing on a five is independent of other throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Timothy creates a game in which the player rolls 4 dice.
This means that [tex]n = 4[/tex]
The dice can land in 6 numbers, one of which is 5.
This means that [tex]p = \frac{1}{6}[/tex]
What is the probability in this game of having exactly two dice or more land on a five?
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{2} = 0.116[/tex]
[tex]P(X = 3) = C_{4,2}.(\frac{1}{6})^{3}.(\frac{5}{6})^{1} = 0.015[/tex]
[tex]P(X = 4) = C_{4,4}.(\frac{1}{6})^{4}.(\frac{5}{6})^{0} = 0.001[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.116 + 0.015 + 0.001 = 0.132[/tex]
So the correct answer is:
B. 0.132
The probability of having exactly two dice or more land on a five is: 0.132.
To determine the probability of having exactly two dice or more land on a five when rolling four dice, we first need to calculate the probabilities of each possible outcome involving getting at least two fives.
1: Define the basic probabilities
Each die has 6 faces, so the probability ( p ) of rolling a five on a single die is:
[tex]\[ p = \frac{1}{6} \]The probability \( q \) of not rolling a five on a single die is:\[ q = 1 - p = \frac{5}{6} \][/tex]
2: Define the number of dice rolls
We are rolling 4 dice.
3: Calculate probabilities for 0, 1, 2, 3, and 4 fives
We use the binomial distribution formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]where \( n = 4 \), \( p = \frac{1}{6} \), and \( k \)[/tex] is the number of fives rolled.
Probability of rolling exactly 0 fives (\( k = 0 \)):
[tex]\[ P(X = 0) = \binom{4}{0} \left(\frac{1}{6}\right)^0 \left(\frac{5}{6}\right)^4 = 1 \times 1 \times \left(\frac{5}{6}\right)^4 = \left(\frac{5}{6}\right)^4 \][/tex]
Probability of rolling exactly 1 five (\( k = 1 \)):
[tex]\[ P(X = 1) = \binom{4}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 \]Probability of rolling exactly 2 fives (\( k = 2 \)):\[ P(X = 2) = \binom{4}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^2 = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 \][/tex]
[tex]Probability of rolling exactly 3 fives (\( k = 3 \)):\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \])^1 \]Probability of rolling exactly 4 fives (\( k = 4 \)):[/tex]
[tex]\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \][/tex]
4: Sum probabilities for \( k \geq 2 \)
We need to find \( P(X \geq 2) \), which is:
[tex]\[ P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \][/tex]
5: Perform calculations
[tex]\[P(X = 0) = \left(\frac{5}{6}\right)^4 \approx 0.4823\]\[P(X = 1) = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{125}{216}\right) \approx 0.3858\]\[P(X = 2) = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} \approx 0.1157\][/tex]
[tex]\[P(X = 3) = 4 \times \left(\frac{1}{6}\right)^3 \times \frac{5}{6} = 4 \times \frac{1}{216} \times \frac{5}{6} = \frac{20}{1296} \approx 0.0154\]\[P(X = 4) = \left(\frac{1}{6}\right)^4 = \frac{1}{1296} \approx 0.0008\][/tex]
6: Summing up [tex]\( P(X \geq 2) \)[/tex]
[tex]\[P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \approx 0.1157 + 0.0154 + 0.0008 = 0.1319\][/tex]
Rounding this to three decimal places, we get 0.132.
Thus, the probability of having exactly two dice or more land on a five is:
[tex]\[ \boxed{0.132} \][/tex].
A 33 m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36 m . Find the length of the shadow. If necessary, round your answer to the nearest tenth.
Answer:
Hypotenuse = 36 Leg = 33
other leg^2 = 36^2 - 33^2
other leg^2 = 207
other leg = 14.3874945699
other leg = 14.4 (rounded)
Step-by-step explanation:
Range of f(x)=-(x-5)^2+9
Answer: (5, -9)
Step-by-step explanation:
Rewrite the equation in term of x and y.
In studying a random sample of 20 automotive batteries, the confidence interval (0.22,0.33) was constructed for the population standard deviation of the batteries' reserve capacity in hours. This population standard deviation should be less than 0.26 hour. Does the confidence interval suggest that the variation in the batteries' reserve capacities is at an acceptable level? Explain your reasoning.
Answer:
NO.
Step-by-step explanation:
From the question, we are given a random sample of 20 automotive batteries, a confidence interval =(0.22,0.33). Also, the population standard deviation is said to be less than 0.26 hour.
The confidence interval does NOT suggest that the variation in the batteries' reserve capacities is at an acceptable level.
REASON: If you look at the confidence interval, we can see that it contains the value for the standard deviation that is 0.26 and even MORE value than 0.26.
This does not give us any suggestion that the standard deviation is less than 0.26.
Final answer:
The confidence interval suggests that the variation in the batteries' reserve capacities is not at an acceptable level because the interval (0.22, 0.33) lies above the acceptable standard deviation of less than 0.26 hour.
Explanation:
In the context of the question, a constructed confidence interval for the population standard deviation of automotive batteries' reserve capacity is (0.22, 0.33 hours). To evaluate whether the variation in the batteries' reserve capacities is at an acceptable level, we would compare the interval to the stated acceptable level of a population standard deviation which should be less than 0.26 hour. Since the lower bound of the interval is above 0.22 and the entire confidence interval lies above 0.26, this suggests that the variability may be higher than the acceptable level, hence the variation is not at an acceptable level according to the specified criteria.
As for the example related to the NeverReady batteries, it demonstrates the use of sample data to question a company's claim about product performance by calculating the probability of obtaining a sample with a mean as low as or lower than observed when assuming that the company's claim is true. If the probability is very low, it casts doubt on the claim.
A chef got 17 bags of onions. The red onions came in bags of 4 and the yellow onions came in bags of 6. If the chef got a total of 88 onions, how many bags of each type of onion did he get?
Answer:
7 bags red onions
10 bags yellow onions
Step-by-step explanation:
If r is the number of bags of red onions, and y is the number of bags of yellow onions, then:
r + y = 17
4r + 6y = 88
Solve the system of equations using substitution or elimination. Using substitution:
r = 17 − y
4(17 − y) + 6y = 88
68 − 4y + 6y = 88
2y = 20
y = 10
r = 7
The chef received 5 bags of red onions and 12 bags of yellow onions.
The question involves solving a system of linear equations to find the number of bags of red onions and yellow onions the chef received. Let's denote the number of bags of red onions as R and the number of bags of yellow onions as Y. We know that:
Each bag of red onions contains 4 onions.
Each bag of yellow onions contains 6 onions.
The chef got a total of 17 bags.
The chef got a total of 88 onions.
Based on this information, we can set up the following equations:
R + Y = 17
(This represents the total number of bags.)
4R + 6Y = 88
(This represents the total number of onions.)
We can solve this system of equations using substitution or elimination. Let's use substitution. First, we can express Y as 17 - R from the first equation:
Y = 17 - R
Now, we substitute Y in the second equation:
4R + 6(17 - R) = 88
By solving this equation, we find that R = 5 and Y = 12. Therefore, the chef got 5 bags of red onions and 12 bags of yellow onions.
What is the volume, in cubic in, of a rectangular prism with a height of 19in, a width
of 17in, and a length of 18in?
Answer:
Use (B*H)H
Step-by-step explanation:
17*18*19
First 17*18= 306
Second is 306*19=5814
*PLS HELP ME WITH MY MATH
The volume of the given rectangular prism will be 5814 inches³.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Volume has units of cube example meter³,cm³, etc.
The volume of the prism = length × height × width.
As per the given,
Length = 18 inches
Width = 17 inches
Height = 19 inches
Volume = 18 x 17 x 19 = 5814 inches³
Hence "The volume of the given rectangular prism will be 5814 inches³".
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Someone ran 2km someone else ran 3,500 meters what would be that combined
Answer:
5,500 meters or 5.5km
Step-by-step explanation:
1 km is = 1000 meter
2km=2000 meters
2000 +3500 =5,5000 meters
A student participates in a Coke versus Pepsi taste test. She correctly identifies which soda is which four times out of six tries. She claims that this proves that she can reliably tell the difference between the two soft drinks. You have studied statistics and you want to determine the probability of anyone getting at least four right out of six tries just by chance alone. Which of the following would provide an accurate estimate of that probability? Remember, you are trying to prove that four out of six is unusual or not unusual if one truly does not know the taste difference.
A. Repeat this experiment with a very large sample of people and calculate the percentage of people who make four correct guesses out of six tries.
B. Simulate this on the computer with the probability of 50% of guessing the correct soft drink on each try, and calculate the percent of times there are four or more correct guesses out of six trials.
C. No need to run any further tests, since 4 out of 6 is better than half of the time, we would say the student's claim is correct.D. Have the student repeat this experiment many times and calculate the percentage of times she correctly distinguishes between the brands
Answer:
A
Step-by-step explanation:
x/-4=-16. Solve for x.
Answer:
64
Step-by-step explanation:
16 *4 is 64 so 64 divide by -4 equals -16.
Hope this helps.
Answer: 64
Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.
On the left side, the -4's will cancel
and on the right side, -16(-4) is 64.
So x = 64.
Please do not try to do this problem in your head.
Show the work that it takes to get x by itself.
Sadie wrote the following on the board find and correct her mistake 2years= 24 weeks
g a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual? A. A residual is a value that is determined exactly, without any error. B. A residual is the amount that one variable changes when the other variable changes by exactly one unit. C. A residual is a value of yminusModifyingAbove y with caret, which is the difference between an observed value of y and a predicted value of y. D. A residual is a point that has a strong effect on the regression equation. b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the ▼ sum of squares sum of the residuals is the ▼ lowest highest possible sum.
Answer:
for the first question we have the "c” as the correct option
residual is a value of y -y^ which is the difference between an observed value of y and predicted value of y
The residual is a value of y -y ^ which is the difference between an observed value of y and predicted value of y, so answer A is false in The residual mo has errors, option B is false because it is not defined as the quantity that changes a variable and it is false that the residual is a point that has a strong effect on the regression
for question two the correct answer is:
the best fitting straight regression line at the scatter plot points is
b) sum of squares and lowest
The residual is the value obtained by subtracting the actual and the predicted value. Therefore, the residual of a linear model can be defined thus ;
Y_actual - Y_predictedThe line if best fit, defines the line which best fits or models a data. It is the line in the the sum of the square is lowest as it tries to minimize the sum of squared error.
Therefore, the correct options are C and (sum of square ; lowest)
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The domain of f(x) = 4x is The range of f(x) = 4x is
Answer:
all real numbers
y>0
Step-by-step explanation:
The range of f(x) = 4x is all real numbers.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Therefore, The range of f(x) = 4x is all real numbers.
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The perimeter of a triangle DEF is 81 units. The length of side DE is twice the length of side EF, and the length of side DF is 4 units less than the length of side DE. Let s represent the length, in units, of side EF. Write an equation that can be used to find s
Answer:
5s = 85
Step-by-step explanation:
Perimeter of our triangle = DE + EF + DF = 81 units
We know from the question that
The length of side DE is twice the length of side EF
DE = 2EF
and the length of side DF is 4 units less than the length of side DE
DF = DE - 4
We can replace EF with s in our equations
DE = 2s
And now we can replace DE from the other equation
DF = DE - 4
DF = 2s - 4
If the perimeter of our triangle = DE + EF + DF = 81 units
We will replace the sides with our new values
Perimeter = 2s + s + 2s - 4 = 81
We can put this as our answer, or we can simplify further
Simplify by adding 4 to both sides
2s + s + 2s - 4 + 4 = 81 + 4
Simplify
2s + s + 2s = 85
Simplify
5s = 85
Since the question only asked for an equation, not for us to solve it, we can stop here
(If you wanted to solve for s, just divide both sides by 5)
5s / 5 = 85 / 5
s = 17
Answer:
81 = s + 2s + (2s -4)
Step-by-step explanation:
In this exercise, we consider finding the first five coefficients in the series solution of the first-order linear initial value problem (x²+2)y′′ − 6y = 0 subject to the initial condition y(0) = 1, y′(0) = 2. Since the equation has an ordinary point at x=0 and it has a power series solution in the form y = Lim(n=0→[infinity])Σ cₙxⁿ.(1) Insert the formal power series into the differential equation and derive the recurrence relation: cn= __________cₙ₋₂ for n=2,3,⋯ The solution to this initial value problem can be written in the form y(x)= c₀y₁(x)+c₁y₂(x) where c₀ and c₁ are determined from the initial conditions. The function y₁(x) is an even function and y₂(x) is an odd function. For this example, from the initial conditions, we have c₀ = ______ and c₁ = ______. The function y₁(x) is an infinite series y₁(x) = 1+ Lim(n=1→[infinity])Σ aₙx²ⁿNote that the constant c₀ has been factored out. (2) Use the recurrence relation to find the first few coefficients of the infinite series: a₂ = _______, a₄ = _______, a₆ = _______, a₈ = _______.Note that the constant c₀ has been factored out. Finally the polynomial y₂(x)= _______NOTE: The function y₂(x) is an odd degree polynomial with first term x. In other words, note that the constant c₁ has been factored out.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation for the answer to the question
Simplify the following expression 1^9
Answer:
1
Step-by-step explanation:
Let f(x)=(3)x−3. Evaluate f(0) without using a calculator.
To evaluate f(0) without using a calculator, simply substitute x with 0 in the function f(x) = 3x - 3 to get f(0) = -3.
Explanation:A mathematical function is a relationship between a set of inputs (domain) and corresponding outputs (range) such that each input is associated with exactly one output. It is a rule or process that assigns a unique value to each input. Functions are fundamental in expressing and analyzing mathematical relationships.
To evaluate f(0) without using a calculator, we can simply replace x with 0 in the given function f(x) = 3x - 3.
Therefore, f(0) = 3(0) - 3 = 0 - 3 = -3.
So, f(0) = -3.
the difference of eight and twice a number
Answer:
8 - 2x
Step-by-step explanation:
Let x be the unknown number
difference is subtraction
8 - 2x
Europeans have been more skeptical than Americans about the use of genetic engineering to improve foods. A sample survey gathered responses from random samples of 824 Americans and 12268 Europeans. (The European sample was larger because Europe is divided into many nations.) Subjects were asked to consider the following issue: Using modern biotechnology in the production of foods, for example to make them higher in protein, keep longer, or change in taste. They were asked if they considered this "risky for society." In all, 432 of Americans and 7629 of Europeans thought the application was risky.
Give a 98% confidence interval for the percent difference (±0.1) between Europe (call them group 1) and the United States:
Answer:
The 98% confidence interval = (-0.14, -0.056)
Explanations:
From the calculations done in the file attached to this solution
Proportions of Americans that considered the application risky = 0.524
Proportions of Americans that did not considerthe application risky = 0.476
Proportions of Europeans that considered the application risky = 0.622
Proportions of Europeans that did not consider the application risky = 0.377
Standard error of the sample proportion using the formula written in the attached file = 0.018
The 98% confidence interval is also calculated as in the attached file and gotten as (-0.14, -0.056)
What are the me and you
What are the x- and y-coordinates of point E, which partitions
the directed line segment from A to B into a ratio of 1:2?
x = ( min )(x2 – x1) + x1
v = l m on Jiva – vi] + vi
(0, 1)
0 (-1,3)
* (-2,5)
(1,0)
Complete question:
What are the x- and y- coordinates of point E, which partitions the directed line segment from [tex]A\:(- 4,\:9) \:to\: B\:(2,\:- 3)[/tex] into a ratio of 1 : 2.
Answer:
(C) (-2,5)
Step-by-step explanation:
[tex]x = (\dfrac{m}{m+n}) (x_2-x_1) + x_1\\\\y = (\dfrac{m}{m+n}) (y_2-y_1) + y_1[/tex]
[tex](x_1,y_1)=(- 4,\:9),(x_2,y_2)=B\:(2,\:- 3)[/tex]
m=1, n=2
[tex]x = \left(\dfrac{1}{1+2}\right) (2-(-4)) + (-4)\\=\left(\dfrac{1}{3}\right) (2+4)-4\\=\left(\dfrac{6}{3}\right)-4=2-4\\x=-2[/tex]
[tex]y = \left(\dfrac{1}{1+2}\right) (-3-9) + 9\\=\left(\dfrac{1}{3}\right) (-12)+9\\=\left(-\dfrac{12}{3}\right)+9=-4+9\\y=5[/tex]
The x- and y-coordinates of the point E is (-2,5)
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 2 and less than 5. The probability of being dealt a card greater than 2 and less than 5 is........
Final answer:
The probability of being dealt a card greater than 2 and less than 5 from a standard deck of 52 cards is 2/13.
Explanation:
The probability of being dealt a card greater than 2 and less than 5 from a standard 52-card deck means you are looking for 3s and 4s from each suit (hearts, spades, clubs, diamonds).
For each suit, there is one 3 and one 4, making a total of 8 possible cards (2 cards per suit multiplied by 4 suits). To calculate the probability, you divide the number of favorable outcomes by the number of possible outcomes. So, this probability is 8/52, which simplifies to 2/13 when reduced.
Translate the sentence into an inequality.
Six subtracted from c is at least 20.
Answer:
6 - c </= 20
Step-by-step explanation:
What algebraic expression must be subtracted from the sum of Y squared plus 5Y -1 and 3Y squared minus 2Y +4 to give you 2Y squared plus 7Y -2
Answer:
The required expression is:
2Y² - 4Y + 5
Step-by-step explanation:
Given the expression:
(Y² + 5Y - 1) + (3Y² - 2Y + 4)
= 4Y² + 3Y + 3
Subtracting (2Y² - 4Y + 5), we have
2Y² + 7Y - 2
Therefore, the expression:
2Y² - 4Y + 5
must be subtracted from the expression:
(Y² + 5Y - 1) + (3Y² - 2Y + 4)
to give the expression:
2Y² + 7Y - 2
For what value of a does 9=(1/27)^2+3
Answer:
if a= (1/27)^2 + 3, then a is about 3.00137
Step-by-step explanation:
I assume you have a typo here.
Your equation should be a = (1/27)^2 + 3 ...
If that is so, a = (1/27)^2 + 3 = 3.00137...
What is the relationship between 1 and 2
Answer:
they are a complimentary couple since both offer examples of their own qualities. Both types are highly dutiful and are attracted to each other
Step-by-step explanation:
hope this helps
~berrian
Final answer:
The relationship between 1 and 2 in mathematics can refer to causality, ratios, probability, physical properties in physics, or reciprocal relationships, depending on the context.
Explanation:
The relationship between 1 and 2 can refer to various mathematical concepts, depending on the context in which these numbers are being used. Here are a few examples:
Causality: In a simple model with objects A and B, an arrow from A to B implies that A is the cause and B is the effect. It's a directional relationship.
Ratio: When we say the ratio between two quantities is 1:2, it implies for every unit of the first quantity, there are two units of the second quantity. In this case, RP1 to Rp2 is 1:2.
Probability: In the context of dice, if the first value is 2, the ratio could describe the possible outcomes when rolling two dice.
Physical properties: Mathematical relationships can be determined for variable pairs in physics such as Pressure (P) versus number of moles (n), or volume (V) versus temperature (T).
Reciprocity: In some mathematical expressions, swapping the subscripts '1' and '2' does not change the relationship, indicating a reciprocal or bidirectional relationship between the two.
Understanding these relationships requires recognizing the context and the mathematical principles that govern them.
Which two temperatures have a 0 degrees Celsius?
A large van has careened off the road into a ditch, and two tow trucks are attempting to winch it out. The cable from the first winch exerts a force of 900 lb, while the cable from the second exerts a force of 700 lb. Determine the angle of theta for the first truck that will bring the van directly out of the ditch and along the resultant.
Answer:
25
Step-by-step explanation:
The distance between two cities on a map is 13 cm. What is the actual distance between the cities if the map is drawn at a scale of 1:50,000?
Answer:
65,000
Step-by-step explanation:
because the scale is 1:50,000, so just simply multiply by 50,000.
Answer:i am not going to answer htis question 4 u but i will tell u how 2 do it first u mulitply 50,000 by 13 then you convert the number of centimeters u get into kilometers (this is where most people get wrong cuz there 2 lazy to read the question.
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. Using the empirical rule, what percentage of the boys are between 65 and 75 inches tall?
Answer:
68%
Step-by-step explanation:
Final answer:
Using the empirical rule for normal distribution, approximately 68% of the boys at the all boys school with a mean height of 70 inches and a standard deviation of 5 inches are between 65 and 75 inches tall.
Explanation:
According to the empirical rule (also known as the 68-95-99.7 rule), for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
And around 99.7% falls within three standard deviations of the mean.
In the case of the all boys school with a mean height of 70 inches and standard deviation of 5 inches, the range between 65 inches (70 - 5) and 75 inches (70 + 5) represents one standard deviation from the mean on either side. Thus, using the empirical rule, approximately 68% of the boys are between 65 and 75 inches tall.