Question

A consumer group did a study to determine if the college students at Harvard and MIT have increased rents significantly in Cambridge compared to other towns in the Boston area. Assume that they took a sample of 49 apartments from town and that they know that the population mean is $420 and the population standard deviation of $105. What is the probability that the sample mean for the 49 houses is between $400 and $450? How would you solve this in excel?

Answer 1

Using central limiting theorem we define the standard random variable Z as

where is the sample mean

Now the required probability is

--------------(1)

Using Excel command   which gives cummulative probability we get

and

Hence by (1) we get