The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be at least $1,500 per month? The standard deviation of the sample is $300.
A) 34.13%
B) 84.13%
C) 50%
D) 100%

Question

Quizplus · Accepted Answer

Given the sample size (n=36) and the sample mean ($2,000), even if the distribution of the monthly costs is positively skewed, the Central Limit Theorem applies because the sample size is large enough (n ≥ 30). This theorem states that the sampling distribution of the sample mean will be approximately normally distributed regardless of the shape of the population distribution. The question asks for the probability of finding a sample mean of at least $1,500, which is significantly below the population mean of $2,000. Given the standard deviation of the sample ($300) and the large difference between the population mean and the $1,500 value, the probability of a sample mean being at least $1,500 is extremely high, essentially approaching 100%. This is because, according to the Central Limit Theorem, it's highly unlikely for a sample mean of 36 apartments to deviate so far from the population mean to fall below $1,500.

The Mean Rent for a Two-Bedroom Apartment in the Greater