Question

Consider the distribution of monthly social security (OASDI) payments. Assume a normal distribution with a standard deviation of $120. If one-fourth of payments are above $1255.94, what is the mean monthly payment?

A) $1155.94
B) $1235.94
C) $1355.94
D) $1435.94

Answer 1

To find the mean monthly payment, use the z-score formula to determine the value of one-fourth of the payments above $1255.94. The mean monthly payment is $1235.94.

Step-by-step explanation:

To find the mean monthly payment, we need to determine the value of one-fourth of the payments above $1255.94. Since the distribution is normal, we can use the z-score formula to find the corresponding z-score. The z-score formula is given by: z = (x - mean) / standard deviation.

From the question, we know that one-fourth of the payments are above $1255.94. This means that the z-score corresponding to $1255.94 is 0.25. We can rearrange the z-score formula to solve for the mean:

mean = x - (z * standard deviation)

Substituting the values, we get:

mean = $1255.94 - (0.25 * $120)

mean = $1235.94

Therefore, the mean monthly payment is $1235.94.