The probability that the sample mean is less than 74 is about 10.38%.
To solve the problem step-by-step, let's go through each calculation in detail:
1. Compute the Standard Error (SE):
Given:
- Population mean [tex](\(\mu\))[/tex] = 75
- Population standard deviation [tex](\(\sigma\))[/tex] = 5
- Sample size (n) = 40
The standard error of the mean is calculated using the formula:
[tex]\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \][/tex]
Substituting the given values:
[tex]\[ \text{SE} = \frac{5}{\sqrt{40}} = \frac{5}{6.3246} \approx 0.791 \][/tex]
2. Compute the Z-score for a sample mean of 74:
The Z-score is calculated using the formula:
[tex]\[ Z = \frac{X - \mu}{\text{SE}} \][/tex]
Where:
- (X) is the sample mean.
Given (X = 74):
[tex]\[ Z = \frac{74 - 75}{0.791} = \frac{-1}{0.791} \approx -1.26 \][/tex]
3. Find the probability corresponding to the Z-score:
The Z-score of -1.26 corresponds to the cumulative probability from the standard normal distribution table.
A Z-score of -1.26 gives a cumulative probability (area under the curve to the left of the Z-score) of approximately 0.1038.
Therefore, the probability that the sample mean is less than 74 is about 10.38%.
In the triangle below, what ratio is cos θ?
Answer:
[tex]cos(theta)=\frac{5}{13}[/tex]
Ratio is 5:13
Step-by-step explanation:
We are given with right angle triangle with side lengths
cos theta ratio is adjacent side divide by hypotenuse
In the triangle , adjacent side for theta is 5 and hypotenuse is 13
[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(theta)=\frac{5}{13}[/tex]
Find the measure of the central angle with a radius of 18 inches and the area of a sector measuring 40.5π square inches.
Find the area
A. 54 in
B. 36 in
C. 18 in
D. 324 in
(In pie)
area of a circle = pi r^2
radius = 18
so R62 = 18^2 = 324
since you want the answer in pi it would be 324PI
so the answer is 324
How many of each position fantasy football?
In standard fantasy football, each team incorporates a variety of positions including a Quarterback, Running Backs, Wide Receivers, a Tight End, a Flex, Defense/Special Teams, a Kicker and bench spots.
Explanation:In standard fantasy football, each team is composed of a variety of positions: 1 Quarterback (QB), 2 Running Backs (RB), 2 Wide Receivers (WR), 1 Tight End (TE), 1 Flex (which can be a RB, WR, or TE), 1 Defense/Special Teams (DST), and 1 Kicker (K). In most cases, you also have bench spots for subs or injured players, usually 6-7. These numbers can vary depending on the rules of your fantasy league.
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Show me how to make 33 in four different ways
What are the coordinates of the vertices of ABC? Use the coordinates to find the lengths of ab and . bc
The coordinates of the vertices of the triangle are A ( 2 , 2 ) , B ( 6 , 2 ) and C ( 2 , -1 )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the coordinates of the triangle are
A ( 2 , 2 ) , B ( 6 , 2 ) and C ( 2 , -1 )
And , length of AB is given by the distance formula .
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
AB = √ ( 16 + 0 ) = 4 units
BC = √ ( 16 + 9 ) = 5 units
Hence , the lengths of AB and BC are 4 and 5 units respectively
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what is the value of the 2 in 258,364
The digit 2 in the number 258,364 stands for two hundred thousand, occupying the hundred thousands place in the place value system.
The value of the 2 in the number 258,364 represents two hundred thousand. In place value terms, this means the 2 is in the hundred thousands place. To understand this concept clearer, consider the alignment of digits in each place value when written in a column:
2 is in the hundred thousands place (200,000)
5 is in the ten thousands place (50,000)
8 is in the thousands place (8,000)
3 is in the hundreds place (300)
6 is in the tens place (60)
4 is in the ones place (4)
Therefore, the digit 2 represents 200,000.
Answer:
In the number 258,364, the 2 is in the hundred thousand's place. So, its place value is 2 * 100,000 = 200,000.
Explanation:
In the number 258,364, each digit's place value is determined by its position relative to the decimal point. The 2 is in the hundred thousand's place, representing 200,000. In whole numbers, the place values increase from right to left, with each place being 10 times the value of the place to its right. So, the hundred thousand's place has a value of 100,000. Thus, the digit 2 in this position contributes 200,000 to the total value of the number 258,364, indicating that there are 200,000 hundred thousands in it.
Question:
What is the place value of the 2 in 258,364?
The image is the result of an isometric transformation of its pre-image because _____.
a reflection has occurred
a rotation has occurred
the two triangles are congruent
a dilation has occurred
2.31x-4.52/7.54-11.32=6.21
On a certain marathon course a runner reaches a big hill that is at least 10 miles into the race. If a total marathon is 26.2 miles, how can u find the number of miles the runner still has to go?
marathon = 26.2
hill is at least 10
26.2-10=16.2
X= miles left
X<=16.2
Add 43.688 + 127.859?
wxyz is a rectangle, what is zx
the midpoint formula
the fraction 1/9 produces a repeating decimal 0.1 ? true or false
Is the standard deviation of the sample a good estimate of the variation of salaries of tv personalities in general?
The correct answer to this would be:
“No, because the sample is not representative of the whole population.”
Since the sample values are the 10 highest annual salaries of TV personalities, they give almost no information about the salaries of TV personalities as a whole or in general.
The standard deviation of a sample can indicate the variation in salaries of TV personalities, but may not always be accurate if the sample isn't representative or if outliers exist. The median salary is often a better measure for skewed distributions, and multiple statistics should be reported to fully describe economic data.
When considering the variation of salaries of TV personalities, the standard deviation of a sample is a crucial statistic that helps understand the dispersion around the mean salary. However, if the sample is not representative of the entire population or if there are outliers, such as extremely high salaries among TV personalities, it may not be a good estimate of the variation in general. The median salary might provide a more accurate descriptor of the central tendency, especially in a skewed distribution.
It is possible for the standard deviation to be greater than the average in cases where there is a significant spread of values, including outliers. For example, if a few TV personalities earn vastly more than others, it will increase the standard deviation. Additionally, the likelihood of the average salary of a larger group falling within a certain range is determined by the mean and standard deviation. If the distribution is normal, salaries will tend to cluster around the mean, which is why certain salary ranges are expected to be more common.
In a scenario where two companies wish to compare the average salaries of their employees, statistical tests that consider both the mean and standard deviation can help determine if there is a significant difference between the two. Similarly, when evaluating how long employees stay with a company, a study with the average time and associated standard deviation for each company would provide insight into retention rates.
When reporting salaries or any economic data, it is often wise to report multiple measures of central tendency and dispersion, such as the mean, median, and standard deviation, to provide a comprehensive view. This approach takes into account the full range of values, including any potential outliers or skewness in the distribution.
The bear population increases at a rate of 2% each year. There are 1573 bears this year. Which function models the bear population?
The solution is, the growth factor b is, 1.02
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Using the formula:
P = P0(1+r)^t
where
P0 is the initial population
r is the rate in decimal
b = 1+r is the growth factor
t is the time in years.
As per the statement:
the bear population increases at a rate of 2% each year there are 1573 bears this year,
⇒P0 = 1573,
r = 2% = 0.02
then;
solving using the formula,
we get,
⇒ b = 1.02
Therefore, the growth factor b is, 1.02.
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what is the solution to -1 -7 ?
If i have 1 cookie and my buddy has another cookie and i steal his cookie.. how many cookies do i have?
The mathematics problem set with cookies deals with basic addition: if you have 1 cookie and you take another from a friend, you have a sum of 2 cookies.
Explanation:The subject here is basic arithmetic, a branch of mathematics.
If you start with 1 cookie (your own), and then you take || 'steal' || another cookie from your friend, you are basically adding that 1 cookie to the 1 cookie you already have. So, 1 cookie (yours) + 1 cookie (your friend's) = 2 cookies. Hence, you would have 2 cookies.
Remember, in real life, it's not nice to steal. This is just a math problem to help you understand the concept of addition.
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One eighth of the students in the seventh grade are in the school band there are fourty four students in the school band find the number of students in the seventh grade
A test consists of 10 problems and students are told to answer any 4 of these questions. In how many different ways can they choose the 4 questions?
Find the distance between B and E. Simplify completely.
B is (-3,2) E is (4,-2)
4-(-3) = 4+3 =47
-2 -2 = -4
7^2 = 49
-4^2 = 16
Sqrt( 49+16)
Sqrt(65) = 8.062
Round off to 8
Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16).
What is the y-value of P'?
Battery was charged. when the charging began it was 23% full after 30 minutes of charging the battery was 89% full. how fast was the battery charged? How long did it take the battery to be funny charged?
Answer:
The battery was charged at a rate of 2.2 % per minute.
It took 35 minutes to fully charge the battery
Step-by-step explanation:
Initial amount of charge = 23%
Charge after 30 minutes = 89%
Percentage of charge gained in 30 minutes = 89-23
= 66 %
Charging speed of battery = [tex]\frac{percentage\hspace{3}of\hspace{3}charge\hspace{3}gained}{time\hspace{3}taken\hspace{3}in\hspace{3}minutes}[/tex]
= [tex]\frac{66}{30}[/tex]
= 2.2 % per minute
2.2% charge takes 1 minutes
1% charge takes [tex]\frac{1}{2.2}[/tex] minutes
Initially it was 23% charged so it needs 77% more charge to be fully charged.
So, 77% charge takes [tex]\frac{1}{2.2}*77[/tex] minutes
= [tex]\frac{100}{2.2}[/tex] minutes
= 35 minutes
I spent 20% of my weekly income on food. What was my weekly income if I spent $186 ?
If I spent $186. Then my weekly income will be $930.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
I spent 20% of my weekly income on food.
If I spent $186.
Then my weekly income will be
Let x my weekly income.
0.2x = $186
x = $930
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In mostar, bosnia, the ultimate test of a young man's courage once was to jump off a 400-year-old bridge (now destroyed) into the river neretva, 23 m below the bridge. (a) how long did the jump last?
To solve this problem, we must assume that the man undergoes constant acceleration as he goes down the river (therefore no other forces must act on him except gravity). Therefore we can use the formula below to calculate for the duration of his fall:
y = y0 + v0 t + 0.5 a t^2
where y is the distance and y0 = 0 since we set the reference point at the bridge, v0 is the initial velocity and is also equal to v0 = 0 since the man started from rest, therefore the equation becomes:
y = 0 + 0 t + 0.5 a t^2
y = 0.5 a t^2
Rewriting in terms of t:
t^2 = 2 y / a
t = sqrt (2y / a)
a is acceleration due to gravity = 9.8 m/s^2
t = sqrt [2 * 23 / 9.8]
t = 2.17 s
Therefore the jump last only about 2.17 seconds.
State whether the given measurements determine zero, one, or two triangles. b = 84°, b = 28, c = 25
The solution to the system of equation below is (-2,-1).
2x - 3y =-1
11x - 9y =-13
When the first equation is multiplied by -3 the sum of the two equations is equivalent to 5x= -10
Which system of equations will also have a solution of (-2,-1)
Answer:
A
Step-by-step explanation:
edge 2020 Dec 14
There is a state soccer tournament with 128 teams competing for 1st place. Each week, half of the teams get eliminated. How many teams remain after 6 weeks?
A.
16
B.
8
C.
4
D.
2
last one help. Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
A. 645 m2; 812 m2
B. 668 m2 ; 704m2
C. 645 m2; 740 m2
D. 668 m2; 740 m2
Find the indicated probability. round to three decimal places. a test consists of 10
a. True
b. False questions. to pass the test a student must answer at least 6 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?
To answer this problem, we use the binomial distribution formula for probability:
P (x) = [n! / (n-x)! x!] p^x q^(n-x)
Where,
n = the total number of test questions = 10
x = the total number of test questions to pass = >6
p = probability of success = 0.5
q = probability of failure = 0.5
Given the formula, let us calculate for the probabilities that the student will get at least 6 correct questions by guessing.
P (6) = [10! / (4)! 6!] (0.5)^6 0.5^(4) = 0.205078
P (7) = [10! / (3)! 7!] (0.5)^7 0.5^(3) = 0.117188
P (8) = [10! / (2)! 8!] (0.5)^8 0.5^(2) = 0.043945
P (9) = [10! / (1)! 9!] (0.5)^9 0.5^(1) = 0.009766
P (10) = [10! / (0)! 10!] (0.5)^10 0.5^(0) = 0.000977
Total Probability = 0.376953 = 0.38 = 38%
There is a 38% chance the student will pass.
The graph of a linear equation may not be a straight line.
A. True
B. False