Terminology Consider the graph of a normal probability distribution of x values with mean μ and standard deviation σ . Answer each of the following statements as true of false. (i) The graph is bell-shaped, with the highest point over the p. (ii) The graph is symmetrical about a vertical line through σ . (iii)The graph crosses the horizontal azis at σ . (iv)The area under the graph to the right of μ is 0.5. (v) The probability that x is between a and b is the area under the curve between a and b.

Question

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Answer 1

Textbook Question

Chapter 7, Problem 1CR

Terminology Consider the graph of a normal probability distribution of x values with mean μ and standard deviation σ . Answer each of the following statements as true of false.

(i) The graph is bell-shaped, with the highest point over the p.

(ii) The graph is symmetrical about a vertical line through σ .

(iii)The graph crosses the horizontal azis at σ .

(iv)The area under the graph to the right of μ is 0.5.

(v) The probability that x is between a and b is the area under the curve between a and b.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(i)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

(ii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

(iii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

(iv)

Expert Solution

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

(v)

Expert Solution

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.

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Answer 2

Textbook Question

Chapter 7, Problem 1CR

Terminology Consider the graph of a normal probability distribution of x values with mean μ and standard deviation σ . Answer each of the following statements as true of false.

(i) The graph is bell-shaped, with the highest point over the p.

(ii) The graph is symmetrical about a vertical line through σ .

(iii)The graph crosses the horizontal azis at σ .

(iv)The area under the graph to the right of μ is 0.5.

(v) The probability that x is between a and b is the area under the curve between a and b.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(i)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

(ii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

(iii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

(iv)

Expert Solution

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

(v)

Expert Solution

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 7, Problem 1CR

Terminology Consider the graph of a normal probability distribution of x values with mean μ and standard deviation σ . Answer each of the following statements as true of false.

(i) The graph is bell-shaped, with the highest point over the p.

(ii) The graph is symmetrical about a vertical line through σ .

(iii)The graph crosses the horizontal azis at σ .

(iv)The area under the graph to the right of μ is 0.5.

(v) The probability that x is between a and b is the area under the curve between a and b.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(i)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

(ii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

(iii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

(iv)

Expert Solution

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

(v)

Expert Solution

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.

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Answer 4

Textbook Question

Chapter 7, Problem 1CR

Terminology Consider the graph of a normal probability distribution of x values with mean μ and standard deviation σ . Answer each of the following statements as true of false.

(i) The graph is bell-shaped, with the highest point over the p.

(ii) The graph is symmetrical about a vertical line through σ .

(iii)The graph crosses the horizontal azis at σ .

(iv)The area under the graph to the right of μ is 0.5.

(v) The probability that x is between a and b is the area under the curve between a and b.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

(i)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

(ii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

(iii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

(iv)

Expert Solution

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

(v)

Expert Solution

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(i)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

(ii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

(iii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

(iv)

Expert Solution

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

(v)

Expert Solution

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.

Answer 8

(i)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

Answer 9

(i)

Expert Solution

Answer 10

(i)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ.” is true or false.

Answer 13

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is bell-shaped, with the highest point over the μ” is true.

Answer 14

Explanation of Solution

The graph of a normal probability distribution is bell-shaped, with the highest point over the μ is true. The data set is normally distributed if most of the values are closer to the mean value, and fewer values are much smaller than mean and much larger than mean.

Answer 15

(ii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

Answer 16

(ii)

Expert Solution

Answer 17

(ii)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ.” is true or false.

Answer 20

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution is symmetrical about a vertical line through σ” is false.

Answer 21

Explanation of Solution

The graph of a normal probability distribution is symmetrical about a vertical line through σ is false statement. As it is symmetrical about a vertical line extending upward from the mean μ..

Answer 22

(iii)

Expert Solution

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

Answer 23

(iii)

Expert Solution

Answer 24

(iii)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is true or false.

Answer 27

Answer to Problem 1CR

Solution: The statement “The graph of a normal probability distribution crosses the horizontal axis at μ+4σ” is false.

Answer 28

Explanation of Solution

The graph of a normal probability distribution crosses the horizontal axis at μ+4σ is false. As the curve approaches the horizontal axis but never touches or crosses it.

Answer 29

(iv)

Expert Solution

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

Answer 30

(iv)

Expert Solution

Answer 31

(iv)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5.” is true or false.

Answer 34

Answer to Problem 1CR

Solution: The statement “The area under the graph of a normal probability distribution to the right of at μ is 0.5” is true.

Answer 35

Explanation of Solution

The area under the graph of a normal probability distribution to the right of at μ is 0.5 is true. As the area under the entire curve is 1, so area under the graph to the right and left of μ is 0.5.

Answer 36

(v)

Expert Solution

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.

Answer 37

(v)

Expert Solution

Answer 38

(v)

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

The statement “The probability that x is between a and b is the area under the curve between a and b” is true or false.

Answer 41

Answer to Problem 1CR

Solution: The statement “The probability that x is between a and b is the area under the curve between a and b” is true.

Answer 42

Explanation of Solution

The probability that x is between a andb is the area under the curve between a and b is true. The curve used to describe the distribution of a continuous random variable is called probability distribution curve. It tells what proportion of the population falls within any given interval.