The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 2.4 cars and a standard deviation of 4. 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 = 2.4 and standard deviation = 4
B)shape unknown with mean = 2.4 and standard deviation = 0.4
C)approximately normal with mean = 2.4 and standard deviation = 0.4
D)shape unknown with mean = 2.4 and standard deviation = 4

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal regardless of the shape of the population distribution, as long as the sample size is sufficiently large (which is generally considered to be the case with n ≥ 30). Here, with a sample size of 100, the sampling distribution of the sample mean will be approximately normal. The mean of the sampling distribution (μx̄) is equal to the population mean (μ), which is 2.4. The standard deviation of the sampling distribution (σx̄), also known as the standard error, is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is 4/√100 = 0.4.

The Number of Cars Running a Red Light in a Day