Question

According to a research​ institution, the average hotel price in a certain year was ​$99.07. Assume the population standard deviation is ​$20.00 and that a random sample of 31 hotels was selected. Complete parts part b below.

a. Calculate the standard error of the mean.=​$3.59

​(Round to two decimal places as​ needed.)

b. What is the probability that the sample mean will be less than ​$101​?_______​(Round to four decimal places as​ needed.)

Answer 1

a)

Standard error of the mean = / sqrt(n)

= 20 / sqrt(31)

= 3.59

b)

Using central limit theorem,

P( < x) = P (Z < x - / )

So,

P( < 101) = P( Z < 101 - 99.07 / 3.59)

= P( Z < 0.5376)

= 0.7046