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 9.79 hours of sleep, with a standard deviation of 1.8 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 6.2 hours of sleep?

(b) What is the probability that a visually impaired student gets between 6.9 and 10.22 hours of sleep?

Answer 1

Solution-A:

X~N(9.79,1.8)

P(X<6.2)

P(Z<6.2-9.79/18)

P(Z<-3.59/18)

P(Z<-0.1994444)

use pnorm function in n R to get the answer:

Rcode:

library(tigerstats)
pnormGC(bound=6.2,region="below",mean=9.79,sd=1.8,graph=TRUE)

0.0231

the probability that a visually impaired student gets less than 6.2 hours of sleep is 0.0231

Solution-b:

P(6.9<X<10.22)

use pnormGC function in R

pnormGC(c(6.9,10.22),region="between",mean=9.79,sd=1.8,graph=TRUE)

The probability that a visually impaired student gets between 6.9 and 10.22 hours of sleep is .5402