The number of violent crimes committed in a day possesses a distribution with a mean of 2.8 crimes per day and a standard deviation of 4 crimes per day. A random sample of 100 days was observed, and the sample mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample means.

The distribution is approximately normal with mean = 2.8 and standard error = 0.4

Step-by-step explanation:

We are given;

Mean; μ = 2.8

Standard deviation; σ = 4

Sample size; n = 100

Now, the central limit theorem states that the sample mean with a sample size(n) from a population mean (μ) and population standard deviation(σ) will, for large value of n, have an approximately normal distribution with mean μ and standard error as (σ/√n)

The sample size is 100 and thus it's very large because it's bigger than minimum of 30 for approximate distribution.

Thus, SE = (σ/√n) = 4/√100 = 4/10 = 0.4

Thus,from the central limit theorem I described, we can say that the distribution is approximately normal with mean = 2.8 and standard error = 0.4

a. she will receive a refund of $278.

step-by-step explanation: