SOLUTION: In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,350 and a standard deviation of $260. The distribution of

Question 1092101: In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,350 and a standard deviation of $260. The distribution of the monthly rent does not follow the normal distribution. In fact, it is positively skewed.

What is the probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Probability ______?

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
First of all, the distribution of sample means of one-bedroom apartments will have a normal distribution even though the distribution of one-bedroom apartments is positively skewed (Central Limit Theorem).
:
Mean μ = 2350
Standard deviation σ = 260
Standard error σ / √ n = 260 / √ 65 = 32.249031
standardize xbar to z = (xbar - μ) / (σ / √ n )
P(xbar > 2260) = P( z > (2260-2350) / 32.249031)
= P(z > -2.7908) = 0.9974
(from normal probability table)
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