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
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