Provide an appropriate response.
-The number of violent crimes committed in a day possesses a distribution with a mean of 3.8 crimes per day and a standard deviation of 2 crimes per day. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.
A) approximately normal with mean = 3.8 and standard deviation = 0.2
B) approximately normal with mean = 3.8 and standard deviation = 2
C) shape unknown with mean = 3.8 and standard deviation = 2
D) shape unknown with mean = 3.8 and standard deviation = 0.2

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 (3.8) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (2/√100 = 0.2).

Provide an Appropriate Response