Using diaries for many weeks, a study on the lifestyles of visually impaired stu

Question

Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.22 hours of sleep, with a standard deviation of 2.06 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(a)  What is the probability that a visually impaired student gets less than 6.6 hours of sleep?

answer:

(b)  What is the probability that a visually impaired student gets between 7 and 9.97 hours of sleep?

answer:

(c)  Thirty percent of students get less than how many hours of sleep on a typical day?

answer:  hours

Explanation / Answer

Ans:

Given that

mean=9.22

standard deviation=2.06

a)

z=(6.6-9.22)/2.06=-1.272

P(X<-1.272)=P(z<-1.272)=0.1018

b)

z(7)=(7-9.22)/2.06=-1.078

z(9.97)=(9.97-9.22)/2.06=0.364

P(-1.078<=z<=0.364)=P(z<=0.364)-P(z<=-1.078)

=0.6421-0.1405

=0.5016

c)P(Z<=z)=0.3

z=-0.5244

x=9.22-0.5244*2.06

x=8.14

i.e 30% of the students get less than 8.14 hrs of sleep.

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