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 under $1,800 per month? The standard deviation of the sample is $300.
A) 34.13%
B) 0%
C) 50%
D) 100%

Question

Quizplus · Accepted Answer

Since the distribution of monthly costs is positively skewed, we cannot use the normal distribution for calculations. Instead, we need to use the Central Limit Theorem, which states that the distribution of sample means will be approximately normal as long as the sample size is sufficiently large (n>30).
The formula for the z-score of sample mean is:
z = (x̄ - μ) / (σ / √n)
where x̄ is the sample mean, μ is the population mean ($2,000), σ is the standard deviation of the population ($300), and n is the sample size (36).
Plugging in the values, we get:
z = (1,800 - 2,000) / (300 / √36) = -2
Using a standard normal distribution table, we find that the area to the left of z = -2 is 0.0228, or 2.28%. Therefore, the probability of finding a sample of 36 two-bedroom apartments with a mean under $1,800 per month is 2.28%, or very close to 0%.

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