The number of violent crimes committed in a day possesses a distribution with a mean of 2.2 crimes per dayand a standard deviation of 6 crimes per day. A random sample of 100 days was observed, and the meannumber of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.
A) approximately normal with mean = 2.2 and standard deviation = 0.6
B) approximately normal with mean = 2.2 and standard deviation = 6
C) shape unknown with mean = 2.2 and standard deviation = 6
D) shape unknown with mean = 2.2 and standard deviation = 0.6

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will be approximately normal due to the Central Limit Theorem, with the same mean as the population mean (2.2) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (6/√100 = 0.6).

The Number of Violent Crimes Committed in a Day Possesses