Question 1

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 100 people. How many would you expect to be taller than 160 cm? Please, round your answer to the nearest integer.

Accepted Answer

We need to find the proportion of people taller than 160 cm and then multiply it by the total number of people (100) to get the expected number of people taller than 160 cm. To find the proportion, we can use the z-score formula:

z = (x - μ) / σ

where x is the height cutoff (160 cm), μ is the mean height (170 cm), and σ is the standard deviation (5 cm).

z = (160 - 170) / 5 = -2

Using a standard normal table or calculator, we find that the proportion of people taller than 160 cm is approximately 0.9772.

Expected number of people taller than 160 cm = proportion * total number of people
= 0.9772 * 100
= 97.72

Rounding to the nearest integer, we get 98 people. Therefore, the best choice is B.

Question 2

Suppose that the diameter of an electric cable is normally distributed, with a mean of 0.80 inches and a standard deviation of 0.01 inches. Suppose that a sample of the cable is randomly selected. What is the probability that the diameter will exceed 0.82 inches? Please round the answer to the nearest thousandth, if necessary.

Accepted Answer

We need to find the probability that the diameter will exceed 0.82 inches. This can be represented as P(X > 0.82), where X is the diameter of the cable. Using the formula for standardizing a normally distributed variable, we get:

Z = (X - μ) / σ

where μ = 0.80, σ = 0.01, and X = 0.82. Substituting the values, we get:

Z = (0.82 - 0.80) / 0.01 = 2

Now, we need to find the area under the standard normal distribution curve to the right of Z = 2. Using the standard normal distribution table or calculator, we find that the area is approximately 0.0228. Therefore, the probability that the diameter will exceed 0.82 inches is 0.0228 or 0.023 (rounded to the nearest thousandth). Hence, the correct answer is E.

Question 3

Finish finding the points to prepare the graph of the equation $y = 2 ^ { x }$ . $( 0 , - - ) , ( 1 , - - ) , ( 2 , - - ) , ( 3 , - - )$

Accepted Answer

The answer of Finish finding the points to prepare the...

Question 4

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 80 people. How many would you expect to be between 165 and 175 cm tall? Please, round your answer to the nearest integer.

Accepted Answer

In a normal distribution, about 68% of the data falls within one standard deviation of the mean. Since 165 cm and 175 cm are one standard deviation below and above the mean (170 cm), respectively, we expect about 68% of the people to fall within this range. With 80 people, 68% of 80 is 54.4, which rounds to 55 people.

Question 5

A Type I error is a decision error that favors acceptance of the hypothesis when it is false.

Accepted Answer

A Type I error occurs when a true null hypothesis is incorrectly rejected, not when a false hypothesis is accepted.

Question 6

Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 32 inches and a standard deviation of 4 inches. About 0.1% of the time, the annual rainfall will be less than how many inches?

Accepted Answer

The z-score corresponding to the bottom 0.1% of a normal distribution is approximately -3.09. Using the formula X = μ + zσ, where μ = 32 and σ = 4, we find X = 32 + (-3.09)(4) = 19.64 inches, which is closest to 20 inches.

Question 7

Graph the equation $y = - x ^ { 2 } + 2$ .

Accepted Answer

The answer of Graph the equation \(y = - x...

Question 8

Sketch the graph of the equation. $y = 5 x ^ { 2 }$

Accepted Answer

The answer of Sketch the graph of the equation. \(y...

Question 9

The first step in a sampling procedure is to gather a sample from the population.

Accepted Answer

The answer of The first step in a sampling procedure...

Question 10

Sketch the graph of the equation. $$y = x ^ { 2 } - 4$$

Accepted Answer

The answer of Sketch the graph of the equation. \[y...

Question 11

Sketch the graph of the equation. $$x = \frac { 1 } { 3 } y ^ { 2 }$$

Accepted Answer

The answer of Sketch the graph of the equation. \[x...

Question 12

Suppose that, for a certain exam, a teacher grades on a curve according to the number line shown below. It is known that the grades follow a normal distribution with a mean of 70 and a standard deviation of 7. There are 45 students in the class. How many students should receive an A? Please, round your answer to the nearest integer.

Accepted Answer

The answer of Suppose that, for a certain exam, a...

Question 13

Choose the correct set of points that prepares the graph of the equation $y = 10 ^ { x }$ for nonnegative values of x.

Accepted Answer

The answer of Choose the correct set of points that...

Question 14

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 4. What is the variance for this experiment of measuring the height of a person?

Accepted Answer

The answer of Suppose that people's heights (in centimeters) are...

Question 15

Suppose that, for a certain exam, a teacher grades on a curve according to the figure shown below. It is known that the grades follow a normal distribution with a mean of 60 and a standard deviation of 4. There are 45 students in the class. What score would be necessary to obtain a B?

Accepted Answer

The answer of Suppose that, for a certain exam, a...

Question 16

Suppose that the diameter of an electric cable is normally distributed, with a mean of 0.85 inches and a standard deviation of 0.01 inches. Suppose that a sample of the cable is randomly selected. What is the probability that the diameter will be greater than 0.84 inches? Please round the answer to the nearest thousandth, if necessary.

Accepted Answer

The answer of Suppose that the diameter of an electric...

Question 17

Sketch the graph of the equation. $y = - 6 x ^ { 2 }$

Accepted Answer

The answer of Sketch the graph of the equation. \(y...

Question 18

A Type I error is a decision error that favors rejectance of the hypothesis when it is true.

Accepted Answer

The answer of A Type I error is a decision...

Question 19

Choose the correct set of points that prepares the graph of the equation $$y = - x ^ { 2 }$$ .

Accepted Answer

The answer of Choose the correct set of points that...

Question 20

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. What is the probability that a person selected at random is taller than 175 cm? Please, round your answer to three decimal places, if necessary.

Accepted Answer

The answer of Suppose that people's heights (in centimeters) are...

Quiz 11: Graphs

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 100 people. How many would you expect to be taller than 160 cm? Please, round your answer to the nearest integer.

Finish finding the points to prepare the graph of the equation $y = 2 ^ { x }$ . $( 0 , - - ) , ( 1 , - - ) , ( 2 , - - ) , ( 3 , - - )$

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 80 people. How many would you expect to be between 165 and 175 cm tall? Please, round your answer to the nearest integer.

A Type I error is a decision error that favors acceptance of the hypothesis when it is false.

Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 32 inches and a standard deviation of 4 inches. About 0.1% of the time, the annual rainfall will be less than how many inches?

Graph the equation $y = - x ^ { 2 } + 2$ . $Graph the equation y = - x ^ { 2 } + 2 .$

Sketch the graph of the equation. $y = 5 x ^ { 2 }$

The first step in a sampling procedure is to gather a sample from the population.

Sketch the graph of the equation. $y = x ^ { 2 } - 4$

Sketch the graph of the equation. $x = \frac { 1 } { 3 } y ^ { 2 }$

Choose the correct set of points that prepares the graph of the equation $y = 10 ^ { x }$ for nonnegative values of x.

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 4. What is the variance for this experiment of measuring the height of a person?

Suppose that, for a certain exam, a teacher grades on a curve according to the figure shown below. It is known that the grades follow a normal distribution with a mean of 60 and a standard deviation of 4. There are 45 students in the class. What score would be necessary to obtain a B?

Sketch the graph of the equation. $y = - 6 x ^ { 2 }$

A Type I error is a decision error that favors rejectance of the hypothesis when it is true.

Choose the correct set of points that prepares the graph of the equation $y = - x ^ { 2 }$ .

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. What is the probability that a person selected at random is taller than 175 cm? Please, round your answer to three decimal places, if necessary.

Quiz 11: Graphs

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 100 people. How many would you expect to be taller than 160 cm? Please, round your answer to the nearest integer.

Finish finding the points to prepare the graph of the equation y=2xy = 2 ^ { x }y=2x . (0,−−),(1,−−),(2,−−),(3,−−)( 0 , - - ) , ( 1 , - - ) , ( 2 , - - ) , ( 3 , - - )(0,−−),(1,−−),(2,−−),(3,−−)

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 80 people. How many would you expect to be between 165 and 175 cm tall? Please, round your answer to the nearest integer.

A Type I error is a decision error that favors acceptance of the hypothesis when it is false.

Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 32 inches and a standard deviation of 4 inches. About 0.1% of the time, the annual rainfall will be less than how many inches?

Graph the equation y=−x2+2y = - x ^ { 2 } + 2y=−x2+2 .

Sketch the graph of the equation. y=5x2y = 5 x ^ { 2 }y=5x2

The first step in a sampling procedure is to gather a sample from the population.

Sketch the graph of the equation. y=x2−4y = x ^ { 2 } - 4y=x2−4

Sketch the graph of the equation. x=13y2x = \frac { 1 } { 3 } y ^ { 2 }x=31​y2

Choose the correct set of points that prepares the graph of the equation y=10xy = 10 ^ { x }y=10x for nonnegative values of x.

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 4. What is the variance for this experiment of measuring the height of a person?

Suppose that, for a certain exam, a teacher grades on a curve according to the figure shown below. It is known that the grades follow a normal distribution with a mean of 60 and a standard deviation of 4. There are 45 students in the class. What score would be necessary to obtain a B?

Sketch the graph of the equation. y=−6x2y = - 6 x ^ { 2 }y=−6x2

A Type I error is a decision error that favors rejectance of the hypothesis when it is true.

Choose the correct set of points that prepares the graph of the equation y=−x2y = - x ^ { 2 }y=−x2 .

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. What is the probability that a person selected at random is taller than 175 cm? Please, round your answer to three decimal places, if necessary.

Finish finding the points to prepare the graph of the equation $y = 2 ^ { x }$ . $( 0 , - - ) , ( 1 , - - ) , ( 2 , - - ) , ( 3 , - - )$

Graph the equation $y = - x ^ { 2 } + 2$ . $Graph the equation y = - x ^ { 2 } + 2 .$

Sketch the graph of the equation. $y = 5 x ^ { 2 }$

Sketch the graph of the equation. $y = x ^ { 2 } - 4$

Sketch the graph of the equation. $x = \frac { 1 } { 3 } y ^ { 2 }$

Choose the correct set of points that prepares the graph of the equation $y = 10 ^ { x }$ for nonnegative values of x.

Sketch the graph of the equation. $y = - 6 x ^ { 2 }$

Choose the correct set of points that prepares the graph of the equation $y = - x ^ { 2 }$ .