Answered: The average time to run the 5K fun run…

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

The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.6 minutes. 42 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected runner is timed, find the probability that this runner's time will be between 23.4982 and 23.8982 minutes.
For the 42 runners, find the probability that their average time is between 23.4982 and 23.8982 minutes.
Find the probability that the randomly selected 42 person team will have a total time less than 1033.2.
For part e) and f), is the assumption of normal necessary? NoYes
The top 15% of all 42 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 amount of money that people spend at Don Mcalds fast food place is $7.0200 with a standard deviation of $1.6900. 11 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
What is the probability that one randomly selected customer will spend less than $7.0056?
For the 11 customers, find the probability that their average spent is less than $7.0056.
Find the probability that the randomly selected 11 customers will spend more than $77.0616.
For part e) and f), is the assumption of normal necessary? YesNo
The owner of Don Mcalds gives a coupon for a free sundae to the 5% of all groups of 11 people who spend the most money. At least how much must a group of 11 spend in total to get the free sundae? $

Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible.

What is the distribution of XX? XX ~ U(,)
Suppose that 37 people are surveyed. What is the distribution of ¯xx¯ for this sample? ¯xx¯ ~ N(,)
What is the probability that the average birth month of the 37 people will be more than 7.7?

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.

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