The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of $250 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 50 one bedroom apartments and finding the mean to be at least $1,950 per month?

The probability is 1.

Explanation:

Despite that the he distribution is positively skewed, the distribution of sample means of one-bedroom apartments  will still be a a normal distribution based on Central Limit Theorem.

Since we have

μ = mean = 2200

SD = standard deviation  = 250

n = sample size = 50

Therefore,

Standard error = SD ÷ √n

                        = 250 ÷ √50

                        = 250 ÷ 7.07106781186548

                        = 35.3553390593274  approximately 35.36

Standardize xbar to z = (xbar - μ) ÷ (SD ÷ √n)

Therefore, we have:

P(xbar > 1,950) = P(z > (1,950 - 2200) ÷ 35.36)

                        = P(z > - 250 ÷ 35.36)                      

                        = P(z > -7.07) = 1

Therefore, the probability of selecting a sample of 50 one bedroom apartments is 1 which can be said to be certain.