please help me with question a, b, and d

Question

 2. 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.

a.) shape unknown with mean of 2.8 and a standard deviation of 0.4 

b.) approximately normal with mean of 2.8 and standard deviation of 4 c.) shape unknown with mean of 2.8 and standard deviation of 4 

d.) approximately normal with mean of 2.8 and standard deviation of 0.4. 

Answer 1

You can apply the Central Limit Theorem to answer this question. Please know that, to use this theorem, we need a large sample size (such as n >= 30). In this case, n = 100 > 30 is large. So the distribution of the mean should follow this theorem with mean = mu and standard deviation = sigma/sqrt(n). Best!