Question

The number of violent crimes committed in a day possesses a distribution with a mean of 4.8 crimes per day and a standard deviation of 2 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 mean.

Answer 1

According to the central limit theorem (n>= 30), the sampling distribution of the sample mean is approximately normal with a mean of 4.8 and a standard deviation of 2.

So:

x = standard dev / sample size

= 2 / 100

= 1/50

= 0.02; it is normal due to its large sample size