Suppose that a category of world dass runners are known to run a marathon (26 mi

Question

Suppose that a category of world dass runners are known to run a marathon (26 mies) in an average of 143 minutes with a standard deviation ons minutes. Consider .9 of the racts w the average (a) Find the median of the average running times. (That is, find the median of the sampling distribution of the average running times.) 143 (b) Find the slowest 10 percent of the average running times.(Round the answer to the second decimal place.) min (e) Find the fastest 10 percent of the average running times.(Round the answer to the second decimal place) min Ask Your Teachen Question Details following. (Give your answers correct to two decimal places) -25.4 and . 4.1 (a) Calculate the z score for an x of 20.1. (b) Calculate the z score for an x of 20.1 from a sample of size 28 (c) Explain how 20.1 can have such different z-scores x and x belong to the same distribution x and x belong to deferent distributions

Explanation / Answer

a)as sample size is greater than 30;

median =mean =143

b)

for slowest 10% ; at 90th percentile z score =1.28

hence slowest 10% time =mean +Z*std deviation =145.38

c)fastest 10% time =mean -Z*std deviation =140.62

4)

a) z score =(X-mean)/std deviation=(20.1-25.4)/4.1=-1.29

b)z score =(X-mean)/std error =(20.1-25.4)/(4.1/28)) =-6.84

c) x and xbar belong to different distribution.

( please revert if any answer mismatches or any clarification)

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