according to the u.s census bureau, the mean of 6 According to the U.S. Census s

Question

according to the u.s census bureau, the mean of 6 According to the U.S. Census s Bureau, the mean of the commute time to work for a resident of Boston. the Massachusetts, is 27.3 minutes. to answer the following: th sume that the standard deviation of the commute time is 8.1 minutes percentage of commuters in Boston has a commute time within 2 standard percentage of commuters in Boston has a commute time within 1.5 standard minimum percentage of commuters who have commute times between 3 minutes and a)- What minimum deviations of the mean? (5pts) (b- What minimum deviations of the mean? (5 pts) (c) What is the 51.6 minutes? (5 pts) 7- Roberto finishes a triathlon (750-meter swim, 5-kilometer rnun, and 20-kilometer bicycle) in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among all women in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better in relation to their gender? (10 pts)

Explanation / Answer

Ans:;

6)Use Chebyshev's therom

At least 11/k^2 of the data lie within k standard deviations of the mean, that is, in the interval with endpoints x¯±ks for samples and with endpoints ±kfor populations, where k is any positive whole number that is greater than 1.

a)here,k=2

so,1-(1/2^2)=1-1/4=3/4=0.75

Hence,atleast 75% of the data lie within 2 standard deviations of mean.

b)

k=1.5

so,1-(1/1.5^2)=1-0.44=0.56

Hence,atleast 56% of the data lie within 2 standard deviations of mean.

c)3 and 51.6 are 3 standard deviations away from the mean.

k=3

so,1-(1/3^2)=1-0.11=0.89

Hence,atleast 89% of the data lie within 2 standard deviations of mean.

7)

z score for Roberto:

z=(63.2-69.4)/8.9=-0.70

P(z<=-0.7)=0.2420

24.2th percentile

z score for Zandra:

z=(79.3-84.7)/7.4=-0.73

P(z<=-0.73)=0.2327

23.27th percentile

z score for Roberto,hence percentile is higher for Roberto,so,Roberto did better.

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