The rent for a one-bedroom apartment in Southern California follows the normal d
ID: 3131497 • Letter: T
Question
The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 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 65 one-bedroom apartments and finding the mean to be at least $2,260 per month?
The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed.
Explanation / Answer
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 2260
u = mean = 2350
n = sample size = 65
s = standard deviation = 260
Thus,
z = (x - u) * sqrt(n) / s = -2.790781528
Thus, using a table/technology, the right tailed area of this is
P(z > -2.790781528 ) = 0.997370952 [ANSWER]