Question

Guests at a Beaumont hotel stay for an average of 9 days with a standard deviation of 2.4 days. Assume that the length of stay is normally distributed. Assume that we select randomly 1000 guests. How many of those guests can be expected to stay between 7 and 14 days

Answer 1

778

Explanation:

We have the length of stay as X

X~N (9,(2.4))

The sample is given as n = 1000

P(7<x<14) is what we are trying to get

P(7-9/2.4 < x-9/2.4 < 14-9/2.4)

= P(-0.83<z<2.08)

P(z<2.08)-p(z<-0.83)

When we go to the z table,

0.981-0.0203

= 0.778

0.778x1000

= 778

So in conclusion, 778 of these guests can be expected to stay between 7 and 14 days.