Question

A population of 1,000 students spends an average of $11.40 a day on dinner. The standard deviation of the expenditure is $4 (a) What is the expected value (in dollars) of the sampling distribution of the sample mean? simple random sample of 64 stu

What is the standard deviation (in dellani) of the sampling distribution of the sample mean? (Round your a
What is the shape of the sampling distribution of the sample mean?
A. exponential
B.skewed to the right
C. uniform
D. normal
E. skewed to the left

Answer 1

The expected value of the sampling distribution of the sample mean is $11.40 and the standard deviation is $0.50. The shape of the sampling distribution of the sample mean is normal.

Step-by-step explanation:

The expected value of the sampling distribution of the sample mean can be calculated using the formula: expected value = population mean = $11.40. So, the expected value of the sampling distribution of the sample mean is $11.40.

The standard deviation of the sampling distribution of the sample mean can be calculated using the formula: standard deviation = population standard deviation / square root of sample size. Given that the population standard deviation is $4 and the sample size is 64, the standard deviation of the sampling distribution of the sample mean is $4 / √64 = $0.50.

The shape of the sampling distribution of the sample mean is normal. This is because the Central Limit Theorem states that for a large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the shape of the population distribution.