Help please!! 2. + 2.23/3.33 points | Previous Answers owskyIntroStat1 7.HW.064.

Question

Help please!!

2. + 2.23/3.33 points | Previous Answers owskyIntroStat1 7.HW.064. Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let R = the average of the 49 races Part (a) Give the distribution of R. (Round your standard deviation to two decimal places) O Part (b) Find the probability that the runner will average between 140 and 145 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min Part (d) Find the median of the average running times. 143 min

Explanation / Answer

mean is 143 and standard error SE is 2

z is given as (x-mean)/s

b) P(140<x<145)=P((140-143)/2<z<(145-143)/2)=P(-1.5<z<2) =P(z<2)-(1-P(z<1.5))

from normal distribution table we get 0.9772-(1-0.9332)=0.9104

c) for 70% the z value from normal distribution table is 0.53

answer is mean+z*s= 143+0.53*2=144.06

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