Help please!! 2 5.56/11.11 points | Previous Answers IllowskylntroStat1 7.HW.064

Question

Help please!!

2 5.56/11.11 points | Previous Answers IllowskylntroStat1 7.HW.064 uppose that a category of world class runners are known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. - the average of the 49 races a Part (a) Give the distribution of X. (Raund your standard deviation to two decimal places.) (147V N a Part (b) Find the probablity that the runner will average between 146 and 150 minutes in these 49 marathons. (Round your answer to four decimal places.) a Part (c) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min a Part (d) Find the median of the average running times. 147 min

Explanation / Answer

Mean is 147 and SE is given as s/sqrt(N)=12/sqrt(49)=12/7=1.7143

b) P(146<x<150)=P((146-147)/1.7143<z<(150-147)/1.7143)=P(-0.58<z<1.75) =P(z<1.75)-(1-P(z<0.58))=0.9599-(1-0.7190)=0.6789

c) for 70th percentile, the z value is 0.53 from the normal distribution table

thus mean+z*SE=147+0.53*1.7143=147.91

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