Question

The state of california has a mean annual rainfall of 22 inches, whereas the state of new york has a mean annual rainfall of 42 inches. assume that the standard deviation for both states is 4 inches. a sample of 35 years of rainfall for california and a sample of 49 years of rainfall for new york has been taken.

Describe the probability distribution of the sample mean annual rainfall for california by specifying its distribution form and parameters.

Answer 1

The probability distribution of the sample mean annual rainfall for California follows a normal distribution with a mean of 22 inches and a standard deviation of 4 inches divided by the square root of 35.

Step-by-step explanation:

The probability distribution of the sample mean annual rainfall for California follows a normal distribution. This is because the sample mean is calculated from a large enough sample size (35 years) and the population standard deviation is known.

The mean of the sample mean annual rainfall for California is equal to the population mean, which is 22 inches. The standard deviation of the sample mean annual rainfall for California, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size.

Therefore, the probability distribution of the sample mean annual rainfall for California is a normal distribution with a mean of 22 inches and a standard deviation of 4 inches divided by the square root of 35.