QUESTION 7 Provide an appropriate response. The number of violent crimes committed in a day possesses a distribution with a mean of 4 crimes per day and a standard deviation of 5 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. shape unknown with mean $=4$ and standard deviation $=5$ approximately normal with mean $=4$ and standard deviation $=0.5$ approximately normal with mean $=4$ and standard deviation $=5$ shape unknown with mean $=4$ and standard deviation $=0.5$ QUESTION 8

Step 1 ：The question is asking for the sampling distribution of the sample mean. According to the Central Limit Theorem, if we have a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normal. The mean of this distribution will be equal to the population mean, and the standard deviation (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Step 2 ：In this case, the population mean is 4 crimes per day, the population standard deviation is 5 crimes per day, and the sample size is 100 days.

Step 3 ：Therefore, the sampling distribution of the sample mean will be approximately normal with a mean of 4 and a standard deviation of 5/sqrt(100) = 0.5.

Step 4 ：The final answer is: The sampling distribution of the sample mean is approximately normal with mean \(=4\) and standard deviation \(=0.5\). So, the correct answer is \(\boxed{\text{approximately normal with mean \(=4\) and standard deviation \(=0.5\)}}\).