The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 4.2 cars and a standard deviation of 6. The number of cars running the red light was observed on 100 randomly chosen days and the mean number of cars calculated. Describe the sampling distribution of the sample mean.
A) approximately normal with mean = 4.2 and standard deviation = 0.6
B) approximately normal with mean = 4.2 and standard deviation = 6
C) shape unknown with mean = 4.2 and standard deviation = 6
D) shape unknown with mean = 4.2 and standard deviation = 0.6

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (n=100 is large), with the same mean as the population mean (4.2) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (6/√100 = 0.6).

The Number of Cars Running a Red Light in a Day