Question

High rent district:the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2544.Assume the standard deviation is 483.A real estate firm samples 83 apartments.Use cumulative distribution table if needed.

What is the probability that the sample mean rent is greater than 2614? Round atleast 4 places

What is the probability that sample mean rent is between 2413 and 2513? Round atleast 4 places

Find the 65th percentile of the sample mean rent? Round 4 places

Would it be unusual if the sample mean were greater than 2610? Round 4 places

Answer 1

Since sample size is large enough, we can approximate the sampling distribution of sample mean by normal distribution.

So, approximately we can write,

or

i)

ii)

iii)

To find  65th percentile of the sample mean rent, i.e. to find x such that

iv)

Since probability i.e. 0.1066 is not quite a small value, we can say that it is not unusual if the sample mean were greater than 2610.