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The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N 25 b. What is the distribution of x? - N( 25 c. What is the distribution of Σα? Σα x-N(350 8.231€) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 08 e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 ✓ 2.2 0.5880 OB OB f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 OF g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N 25 b. What is the distribution of x? - N( 25 c. What is the distribution of Σα? Σα x-N(350 8.231€) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 08 e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 ✓ 2.2 0.5880 OB OB f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 OF g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 53E
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The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 b. What is the distribution of x? - N 25 c. What is the distribution of Σα? Σα - Ν 350 8.2316) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 0° 2.2 0.5880✔ OF e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
Transcribed Image Text:The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 b. What is the distribution of x? - N 25 c. What is the distribution of Σα? Σα - Ν 350 8.2316) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 0° 2.2 0.5880✔ OF e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
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The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 b. What is the distribution of x? - N 25 Or c. What is the distribution of Σx? Σ x-N 350 8.2316) O d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 ✓, 2.2 ✓, 0.5880✔ f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
Transcribed Image Text:The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 b. What is the distribution of x? - N 25 Or c. What is the distribution of Σx? Σ x-N 350 8.2316) O d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 ✓, 2.2 ✓, 0.5880✔ f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
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The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 b. What is the distribution of ? x - N( 25 c. What is the distribution of Σα? Σ x-N 350 8.2316) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 2.2 0.5880✔ OT OF e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
Transcribed Image Text:The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.2 minutes. 14 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 25 b. What is the distribution of ? x - N( 25 c. What is the distribution of Σα? Σ x-N 350 8.2316) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.618 and 25.218 minutes. 0.1084 2.2 0.5880✔ OT OF e. For the 14 runners, find the probability that their average time is between 24.618 and 25.218 minutes. 0.3867 f. Find the probability that the randomly selected 14 person team will have a total time less than 354.2. 0.6950 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 15% of all 14 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
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