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Group 2: It is reported that the mean monthly rent for a one-bedroom apartment w

ID: 3065823 • Letter: G

Question

Group 2:

It is reported that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2,825 and the standard deviation is $575. A real estate firm randomly samples 120 apartments to study. Assume the distribution of monthly rents for a one-bedroom apartment without a doorman is approximately normal. Round all probabilities to three places.

1. Would it be unusual if the sample mean were greater than $3,000? Explain.

2. Would it be unusual for an individual apartment to have a rent more than $3,500? Explain.

Explanation / Answer

Normal distribution params are given below:

Mean = 2825

Stdev = 575

n = 120

1. P(X>3000) = P(Z> (3000-2825)/(575/sqrt(120)) = P(Z>3.33) = .000428 or .000

Since this is less than .05 we say that this it's unusual if sample mean were greater than $3,000

2. P(X>3500) = P(Z> (3000-2825)/575) = P(Z>.304) = .380

Since this is much more than .05 we say that this it's usual if sample mean for a individual apartment to be more than $3500