b. Cluster samples. Stratified random samples. Simple random samples. Question 2

Question

b. Cluster samples. Stratified random samples. Simple random samples. Question 28 0.4 out of 2,751 runners who took part in a 10km race had an average time of 1 hr and 11 minutes. The standard deviation was 12 minutes. Using Chebysheffs theorem,determine at least how many had a running time between 53 minutes and 89 minutes? 0.5 c Using Chebysheff's theor m you have on u erha at least 67.44% of the 2,822 runners took between 59.1 and 77.5 minutes to complete the 10km race. What was the standard deviation of these 2,822 runners?

Explanation / Answer

28) here mean time = 1 hr and 11 minutes =71 minutes

as 53 minute and 89 minute falls k=1.5 std deviaiton away from mean.

therefore proportion of observations falls between 53 and 89 =(1-1/k2) =1-1/1.52 =5/9

hence minimum number of people having had a running time from 53 to 89 inutes =np=2751*5/9 =~1528

29)

here mean =(59.1+77.5)/2 =68.3 minute

for 67.44% ; 0.6744 =1-1/k2

k =1.7525

therefore 77.5 minute falls 1.7525 std deviation away from mean

hence std deviaiton =(77.5-68.3)/1.7525 =5.25

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