statistics

Question

UCLA undergrads sllep a mean of 7 hours a night with a standard deviation of 1.5 hours. Assume sleep time is unimodal and symmetric and refer to the the empirical Rule(68% observations fall within 1 standard deviation of the mean, 95%-2SD,99.7%-3SD)
1A student sleep at the 16th percentile of all the students(meaning sleeps more than 16% of the student and less than 84% of them) how many hours does he/she sleep?
2 what percent of students sleep between 4 and 8.5 hours each night?

Answer 1

Hi Siyuan

 

We have a mean of 7 hours and standard deviation of 1.5 hours

 

Using a standard z table, find the z value when p= 16%.  Looking this up, we have z = -0.995 (you need to interpolate)

 

z = (x - mean)/standard deviation

-0.995 = (x - 7)/1.5

x = 5.5 

Student sleeps 5.5 hours

 

 

For part 2, determine the z value for each of the end points, 4 and 8.5

z = (4-7)/1.5 = -2

z = (8.5-7)/1.5 = 1

 

Look up the probability of each of these z values in the table

P(z=-2) = 0.0228

P(x=1) = 0.8413

 

Percent of students who sleep between 4 and 8.5 hours is 0.8413 - 0.0228 = 0.6185

61.85%