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 9.58 hours of sleep, with a standard deviation of 1 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed. What is the probability that a visually impaired student gets less than 6.3 hours of sleep? What is the probability that a visually impaired student gets between 6.1 and 7.58 hours of sleep? Fourty percent of students get less than how many hours of sleep on a typical day?

Explanation / Answer

Here it is given that mean=9.58 and sd=1 a. P(x<6.3)=P(z<6.3-9.58/1)=P(z<-3.28)= 0.0005

b. P(6.1<x<7.58)=P(-3.48<z<-2)=0.0225

c. P(X<x)=0.40 so using z table we get P(Z<z)=0.40 for z=-0.253=x-9.58/1, so x=9.327

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