Question

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 33. 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.

The number of cars running a red light in a​ day, at a given​ intersection, possesses a distribution with a mean of

4.24.2

cars and a standard deviation of

33.

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.

Answer 1

approximately normal with mean=4.2 and standard deviation=0.3.

The sampling distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, since the population mean is 4.2 cars and the population standard deviation is 3 cars, and we have a sample size of 100 days, then the sampling distribution of the sample mean will have a mean of 4.2 cars and a standard deviation of 3/sqrt(100) = 0.3 cars.

Explanation:

The sampling distribution of the sample mean is the distribution of the mean of a sample of observations from a population. In this case, the sampling distribution of the sample mean would be a normal distribution with a mean of 4.2 and a standard deviation of 33/sqrt(100) = 1.6. This means that 68% of the time, the sample mean would be between 2.6 and 5.8, and 95% of the time, the sample mean would be between 1.6 and 7.8.

The sampling distribution of the sample mean is important because it can be used to make inferences about the population mean. For example, if the sample mean is 5.8, we can be 95% confident that the population mean is between 1.6 and 7.8.