Question

According to a recent survey, 38% of americans get 6 hours or less of sleep each night. If 25 people are selected, find the probability that 14 or more people will get 6 hours or less sleep each night..

Answer 1

There are a number of ways to solve this problem. Here is one.

The standard deviation of a binominal is sqrt(n*p*q) where p is the probability of an event and q is 1-p. So, SD = sqrt(25*.38*.62) = 2.427
The expected number that 6 hours or less is .38*25 = 9.5. Now then (14-9.5)/2.427 = 1.85 standard deviations away from the mean.

Take it from here.

Answer 2

I have the answer in the back of my book and its coming out to be -1.65. I don't understand how is that they are getting that answer?

Answer 3

There are a few steps missing from the above solution. It ended too quickly:
If P(X>=a) then P(X-.5) so P(X=14-.5 or 13.5)
z=13.5-9.5/2.427 = 1.65 = .9505. Since the number is more than take 1-.9505 = .0495
The answer now matches the back of the book.