Statistics: Informed Decisions Using Data (5th Edition)
Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 7, Problem 1RE

(a)

To determine

To identify: The value of μ

(a)

Expert Solution
Check Mark

Answer to Problem 1RE

Solution: The value of μ is 60.

Explanation of Solution

Given: The figure for the probability distribution is provided in the question.

Explanation: μ denotes the mean of the distribution. The provided figure is the curve of the normal distribution. In the provided figure, the distribution is symmetric and the mode of the distribution is at the point 60. Therefore, the point 60 can be considered as the mean of the distribution.

(b)

To determine

To identify: The value of σ

(b)

Expert Solution
Check Mark

Answer to Problem 1RE

Solution: The value of σ is 10.

Explanation of Solution

Given: The figure for the probability distribution is provided in the question.

Explanation: σ denotes the standard deviation of the distribution. The value of the standard deviation can be obtained from the inflection point of the curve. The inflection points for the normal distribution are μσ and μ+σ, where the curvature is changed. In the provided figure, the two inflection points are

μσ=50μ+σ=70

As the value of the mean or μ is 60, so the value of (σ) is obtained from the inflection points and can be calculated as

μσ=50σ=6050σ=10

Conclusion: The provided figure represents the normal curve whose mean (μ) is 60 and (σ) is 10.

(c)

To determine

To interpret: The area under the normal curve when the area right to x=75 is provided.

(c)

Expert Solution
Check Mark

Answer to Problem 1RE

Solution: The provided information can be interpreted as the proportion of the value of the random variable 75 or more is 0.0668. It can be also interpreted as the probability that value of the random variable is 75 or more than 75 is 0.0668.

Explanation of Solution

Given: The figure for the probability distribution is provided in the question. The area covered by the normal curve to the right of the value x=75 is 0.0668.

Explanation: The provided figure represents the normal curve whose mean (μ) is 60 and standard deviation (σ) is 10. The area covered under the normal curve provides the proportion of the value of the random variable as well as the probability of the occurrence of the random variable whose value is greater than or less than that value or in between two values.

On the basis of the provided information, the area covered under the normal curve can be interpreted as the proportion of the value of the random variable is 75 or more is 0.0668 and the probability that the value of the random variable is 75 or more is 0.0668.

(d)

To determine

To interpret: The area under the normal curve when the area right to x=50 and x=75 is provided.

(d)

Expert Solution
Check Mark

Answer to Problem 1RE

Solution: The provided information can be interpreted as the proportion of the value of the random variable that is between 50 and 75 is 0.7745. It can be also interpreted as the probability that value of the random variable lies between 50 and 75 is 0.7745.

Explanation of Solution

Given: The figure for the probability distribution is provided in the question. The area covered by the normal curve between the values x=50 and x=75 is 0.7745.

Explanation: The provided figure represents the normal curve whose mean (μ) is 60 and standard deviation (σ) is 10. The area covered under the normal curve provides the proportion of the value of the random variable as well as the probability of the occurrence of the random variable whose value is greater than or less than that value or in between two values.

On the basis of the provided information, the area covered under the normal curve can be interpreted as the proportion of the value of the random variable that takes values between 50 and 75 is 0.7745 and the probability that the value of the random variable lies between the value 50 and 75 is 0.7745.

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Chapter 7 Solutions

Statistics: Informed Decisions Using Data (5th Edition)

Ch. 7.1 - For Problems 7–12, determine whether the graph can...Ch. 7.1 - For Problems 7–12, determine whether the graph can...Ch. 7.1 - Problems 13–16 use the information presented in...Ch. 7.1 - Prob. 14AYUCh. 7.1 - Prob. 15AYUCh. 7.1 - Prob. 16AYUCh. 7.1 - 17. Uniform Distribution The random-number...Ch. 7.1 - Prob. 18AYUCh. 7.1 - In Problems 19–22, determine whether or not the...Ch. 7.1 - Prob. 20AYUCh. 7.1 - In Problems 19–22, determine whether or not the...Ch. 7.1 - In Problems 19–22, determine whether or not the...Ch. 7.1 - 23. One graph in the figure on the following page...Ch. 7.1 - Prob. 24AYUCh. 7.1 - In Problems 25–28, the graph of a normal curve is...Ch. 7.1 - Prob. 26AYUCh. 7.1 - In Problems 25–28, the graph of a normal curve is...Ch. 7.1 - Prob. 28AYUCh. 7.1 - In Problems 29 and 30, draw a normal curve and...Ch. 7.1 - Prob. 30AYUCh. 7.1 - NW 31. You Explain It! Cell Phone Rates Monthly...Ch. 7.1 - Prob. 32AYUCh. 7.1 - 33. You Explain It! Birth Weights The birth...Ch. 7.1 - Prob. 34AYUCh. 7.1 - NW 35. You Explain It! Gestation Period The...Ch. 7.1 - Prob. 36AYUCh. 7.1 - Prob. 37AYUCh. 7.1 - 38. Heights of Five-Year-Old Females The following...Ch. 7.1 - Prob. 39AYUCh. 7.2 - 1. A random variable Z that is normally...Ch. 7.2 - 2. The notation zα is the z-score such that the...Ch. 7.2 - 3. If X is a normal random variable with mean 40...Ch. 7.2 - Prob. 4AYUCh. 7.2 - In Problems 5–12, find the indicated areas. For...Ch. 7.2 - Prob. 6AYUCh. 7.2 - In Problems 5–12, find the indicated areas. For...Ch. 7.2 - In Problems 5–12, find the indicated areas. For...Ch. 7.2 - In Problems 5–12, find the indicated areas. For...Ch. 7.2 - Prob. 10AYUCh. 7.2 - In Problems 5–12, find the indicated areas. For...Ch. 7.2 - Prob. 12AYUCh. 7.2 - In Problems 13–18, find the indicated z-score. Be...Ch. 7.2 - Prob. 14AYUCh. 7.2 - In Problems 13–18, find the indicated z-score. Be...Ch. 7.2 - In Problems 13–18, find the indicated z-score. Be...Ch. 7.2 - In Problems 13–18, find the indicated z-score. Be...Ch. 7.2 - Prob. 18AYUCh. 7.2 - In Problems 19–22, find the value of zα. NW 19....Ch. 7.2 - Prob. 20AYUCh. 7.2 - In Problems 19–22, find the value of zα. 21....Ch. 7.2 - Prob. 22AYUCh. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - Prob. 26AYUCh. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - Prob. 28AYUCh. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - Prob. 30AYUCh. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - In Problems 23–32, assume that the random variable...Ch. 7.2 - In Problems 33–36, assume that the random variable...Ch. 7.2 - Prob. 34AYUCh. 7.2 - In Problems 33–36, assume that the random variable...Ch. 7.2 - Prob. 36AYUCh. 7.2 - 37. Egg Incubation Times The mean incubation time...Ch. 7.2 - 38. Reading Rates The reading speed of sixth-grade...Ch. 7.2 - Prob. 39AYUCh. 7.2 - 40. Wendy's Drive-Through Fast-food restaurants...Ch. 7.2 - 41. Gestation Period The lengths of human...Ch. 7.2 - Prob. 42AYUCh. 7.2 - Prob. 43AYUCh. 7.2 - Prob. 44AYUCh. 7.2 - Prob. 45AYUCh. 7.2 - Prob. 46AYUCh. 7.2 - NW 47. Egg Incubation Times The mean incubation...Ch. 7.2 - Prob. 48AYUCh. 7.2 - Prob. 49AYUCh. 7.2 - Prob. 50AYUCh. 7.2 - Prob. 51AYUCh. 7.2 - Prob. 52AYUCh. 7.2 - 53. Give three interpretations for the area under...Ch. 7.2 - Prob. 54AYUCh. 7.2 - Prob. 55AYUCh. 7.2 - Prob. 56AYUCh. 7.3 - 1. A _______ _________ ______ is a graph that...Ch. 7.3 - Prob. 2AYUCh. 7.3 - In Problems 3–6, use the results in the table to...Ch. 7.3 - Prob. 4AYUCh. 7.3 - Prob. 5AYUCh. 7.3 - Prob. 6AYUCh. 7.3 - In Problems 7–10, use a normal probability plot to...Ch. 7.3 - In Problems 7–10, use a normal probability plot to...Ch. 7.3 - In Problems 7–10, use a normal probability plot to...Ch. 7.3 - In Problems 7–10, use a normal probability plot to...Ch. 7.3 - Prob. 11AYUCh. 7.3 - Prob. 12AYUCh. 7.3 - Prob. 13AYUCh. 7.4 - 1. In a binomial experiment with n trials and...Ch. 7.4 - 2. When adding or subtracting 0.5 from x, we are...Ch. 7.4 - Prob. 3AYUCh. 7.4 - Prob. 4AYUCh. 7.4 - Prob. 5AYUCh. 7.4 - Prob. 6AYUCh. 7.4 - Prob. 7AYUCh. 7.4 - Prob. 8AYUCh. 7.4 - In Problems 5–14, a discrete random variable is...Ch. 7.4 - Prob. 10AYUCh. 7.4 - Prob. 11AYUCh. 7.4 - Prob. 12AYUCh. 7.4 - Prob. 13AYUCh. 7.4 - Prob. 14AYUCh. 7.4 - Prob. 15AYUCh. 7.4 - Prob. 16AYUCh. 7.4 - Prob. 17AYUCh. 7.4 - Prob. 18AYUCh. 7.4 - In Problems 15–20, compute P(x) using the binomial...Ch. 7.4 - Prob. 20AYUCh. 7.4 - 21. On-Time Flights According to American...Ch. 7.4 - Prob. 22AYUCh. 7.4 - Prob. 23AYUCh. 7.4 - Prob. 24AYUCh. 7.4 - Prob. 25AYUCh. 7.4 - 26. Females Living at Home According to the...Ch. 7.4 - Prob. 27AYUCh. 7.4 - Prob. 28AYUCh. 7 - Prob. 1RECh. 7 - In Problems 2 and 3, draw a standard normal curve...Ch. 7 - In Problems 2 and 3, draw a standard normal curve...Ch. 7 - 4. Find the z-score such that the area to the...Ch. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - In Problems 7–9, draw the normal curve with the...Ch. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 1CTCh. 7 - Prob. 2CTCh. 7 - Prob. 3CTCh. 7 - Prob. 4CTCh. 7 - Prob. 5CTCh. 7 - Prob. 6CTCh. 7 - Prob. 7CTCh. 7 - Prob. 8CTCh. 7 - Prob. 9CTCh. 7 - Prob. 10CTCh. 7 - Prob. 11CTCh. 7 - Prob. 1CSCh. 7 - Prob. 2CS
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