Question

How many in a car? A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that the number of people per car in the population of all cars that enter at this interchange during rush hours has a mean of μ = 1.7 and a standard deviation of σ = 0.85.

Describe the shape of the sampling distribution of x ̅ for SRSs of size n = 125 from the population of all cars that enter this interchange during rush hours. Justify your answer

Answer 1

Let X: Number of people per car in the population of all cars that enter at this interchange during rush hours has a mean and standard deviation

Sample size n = 125

According to the Central limit theorem, for any distribution, if the sample size is 30 or more then the sampling distribution of the sample mean is approximately normal with a mean and standard deviation .

Here sample size is 125 which is more than 30.

So the shape of the sampling distribution of is bell-shaped (normal) that is symmetric.

The parameters of the sampling distribution are,