seh.In which race is Ryan better? 12. Triathlon Roberto finishes a triathlon (75

Question

seh.In which race is Ryan better? 12. Triathlon Roberto finishes a triathlon (750-meter swim, 5-kilometer run, 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? 13. School Admissions A highly selective boarding school will only admit students who place at least 1.5 standard deviations above the mean on a standardized test that has a mean of 200 and a standard deviation of 26. What is the minimum score that an applicant must make on the test to be accepted? 14. Quality Control A manufacturer of bolts has a quality- control policy that requires it to destroy any bolts that are more han 2 standard deviations from the mean. The quality-control ngineer knows that the bolts coming off the assembly line have

Explanation / Answer

#12.
x = 63.2
mean = 69.4, sd = 8.9
Using central limit theorem,
z = (63.2 - 69.4)/8.9 = -0.6966

x = 79.3
mean = 84.7, sd = 7.4
Using central limit theorem,
z = (79.3 - 84.7)/7.4 = -0.7297

As the z-value for Roberto is greater than the z-value for Zandra, Roberto did better.

#13.
mean = 200
sd = 26

Using central limit theorem,
x = mean + z*sigma
x = 200 + 1.5*26 = 239

Hence minimum score is 239.

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