Need help figuring out the last question on this problem. Thanks so much. **5K Run Time Analysis Using Normal Distribution**The average time to run a 5K fun run is 21 minutes with a standard deviation of 2.4 minutes. A sample of 45 runners is randomly selected for analysis. Assume a normal distribution. Answers are rounded to four decimal places.a. **Distribution of Individual Times ($X$)** - $X \sim N(21, 2.4)$b. **Distribution of Sample Mean ($\bar{x}$)** - $\bar{x} \sim N(21, 0.3578)$c. **Distribution of Sum of Times ($\Sigma x$)** - $\Sigma x \sim N(945, 16.0997)$d. **Probability for an Individual's Time** - Probability the runner's time is between 20.7633 and 21.1633 minutes: **0.0664**e. **Probability for the Average Time of 45 Runners** - Probability the average time is between 20.7633 and 21.1633 minutes: **0.4218**f. **Probability of Total Time for 45-Person Team** - Probability the total time is less than 936 minutes: **0.2880**g. **Normality Assumption** - Is normality assumption necessary for (e) and (f)? **Yes**h. **Championship Round Qualification** - For the top 15% of relay races, calculate the longest total time a team can have to qualify for the championship round: - Longest total time: [Calculated Value Needed]**Hint:****Some Helpful Videos:** [Links or descriptions of helpful videos on normal distribution and probability calculations can be included here.]

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Description: Need help figuring out the last question on this problem. Thanks so much. **5K Run Time Analysis Using Normal Distribution**The average time to run a 5K fun run is 21 minutes with a standard deviation of 2.4 minutes. A sample of 45 runners is randoml

The given information is: X~Nμ=21, σ2=2.422 Sample size(n)=45 Further, ∑X~Nnμ=945, nσ2=263.5380

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Statistics

The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.4 minutes. 45 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( 21 |2.4 b. What is the distribution of ? E - N( 21 0.3578 Σ c. What is the distribution of ? æ - N( 945 d. If one randomly selected runner is timed, find the probability that this runner's time will be between 20.7633 and 21.1633 minutes. 0.0664 16.0997 e. For the 45 runners, find the probability that their average time is between 20.7633 and 21.1633 minutor 0 4218

The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.4 minutes. 45 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( 21 |2.4 b. What is the distribution of ? E - N( 21 0.3578 Σ c. What is the distribution of ? æ - N( 945 d. If one randomly selected runner is timed, find the probability that this runner's time will be between 20.7633 and 21.1633 minutes. 0.0664 16.0997 e. For the 45 runners, find the probability that their average time is between 20.7633 and 21.1633 minutor 0 4218

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Need help figuring out the last question on this problem. Thanks so much.

**5K Run Time Analysis Using Normal Distribution**

The average time to run a 5K fun run is 21 minutes with a standard deviation of 2.4 minutes. A sample of 45 runners is randomly selected for analysis. Assume a normal distribution. Answers are rounded to four decimal places.

a. **Distribution of Individual Times ($X$)**
- $X \sim N(21, 2.4)$

b. **Distribution of Sample Mean ($\bar{x}$)**
- $\bar{x} \sim N(21, 0.3578)$

c. **Distribution of Sum of Times ($\Sigma x$)**
- $\Sigma x \sim N(945, 16.0997)$

d. **Probability for an Individual's Time**
- Probability the runner's time is between 20.7633 and 21.1633 minutes: **0.0664**

e. **Probability for the Average Time of 45 Runners**
- Probability the average time is between 20.7633 and 21.1633 minutes: **0.4218**

f. **Probability of Total Time for 45-Person Team**
- Probability the total time is less than 936 minutes: **0.2880**

g. **Normality Assumption**
- Is normality assumption necessary for (e) and (f)? **Yes**

h. **Championship Round Qualification**
- For the top 15% of relay races, calculate the longest total time a team can have to qualify for the championship round:
- Longest total time: [Calculated Value Needed]

**Hint:**

**Some Helpful Videos:** [Links or descriptions of helpful videos on normal distribution and probability calculations can be included here.]

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