The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.6 minutes. 8 runnersare randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible andassume a normal distribution.a. What is the distribution of X? X - N( 242.6b. What is the distribution of ? ī - N( 240.9192c. What is the distribution of > x? > x - N( 1927.3539 v)192o 7.3539d. If one randomly selected runner is timed, find the probability that this runner's time will be between23.7212 and 24.9212 minutes.e. For the 8 runners, find the probability that their average time is between 23.7212 and 24.9212minutes.f. Find the probability that the randomly selected 8 person team will have a total time less than 186.4.g. For part e) and f), is the assumption of normal necessary? O NoO Yesh. The top 15% of all 8 person team relay races will compete in the championship round. These are the15% lowest times. What is the longest total time that a relay team can have and still make it to thechampionship round?minutes

As per guidelines expert have to answer first question three subparts only dear student I have done…

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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This assignment is worth 1 points. The extra point will be added to your overall course grade. For example: if you receive an 88% in the course you can receive up to 1 point giving you a new score of 89%. The following rubric will be used. 0.25 point for drawing the normal distribution curve with the mean value labeled on the curve and the appropriate area shaded. 0.25 point for determining the value of the standard deviation of the sample mean. 0.5 point for finding the correct probability. All work must be shown in order to receive any credit. Please upload your completed assignment here. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.
The avg. … (please complete only part c and d the rest is completed)
I ALREADY HAVE ANSWER ON A,B AND C QUESTION. JUST NEED ANSWER ON D,E,F,G THANKS
The average production cost for major movies is 57 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 57 20 b. What is the distribution of ? - N c. For a single randomly selected movie, find the probability that this movie's production cost is between 52 and 55 million dollars. 58 d. For the group of 46 movies, find the probability that the average production cost is between 52 and 55 million dollars. e. For part d), is the assumption of normal necessary? Yes No
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