The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 50 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( 22 2.6 b. What is the distribution of x? ¤ - N( 22 .3677 v) o Σ c. What is the distribution of ) x? > a x - N( 1100 18.384 v) o o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.9484 and 22.3484 minutes. .0612 e. For the 50 runners, find the probability that their average time is between 21.9484 and 22.3484 minutes. .3841 f. Find the probability that the randomly selected 50 person team will have a total time less than 1070. .0514 g. For part e) and f), is the assumption of normal necessary? O NoO Yes o h. The top 20% of all 50 person team relay races will compete in the championship round. These are the 20% 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 22 minutes and the standard deviation is 2.6 minutes. 50 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( 22 2.6 b. What is the distribution of x? ¤ - N( 22 .3677 v) o Σ c. What is the distribution of ) x? > a x - N( 1100 18.384 v) o o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.9484 and 22.3484 minutes. .0612 e. For the 50 runners, find the probability that their average time is between 21.9484 and 22.3484 minutes. .3841 f. Find the probability that the randomly selected 50 person team will have a total time less than 1070. .0514 g. For part e) and f), is the assumption of normal necessary? O NoO Yes o h. The top 20% of all 50 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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Transcribed Image Text:The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 50 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( 22
2.6
b. What is the distribution of x? ¤ - N( 22
.3677 v) o
Σ
c. What is the distribution of ) x? > a
x - N( 1100
18.384 v) o o
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.9484 and 22.3484 minutes. .0612
e. For the 50 runners, find the probability that their average time is between 21.9484 and 22.3484
minutes. .3841
f. Find the probability that the randomly selected 50 person team will have a total time less than 1070.
.0514
g. For part e) and f), is the assumption of normal necessary? O NoO Yes o
h. The top 20% of all 50 person team relay races will compete in the championship round. These are the
20% 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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