Question

In a large population of adults, the mean IQ is 120 with a standard deviation of 21. Suppose 50 adults are randomly selected for a market research campaign. (Round all answers to 4 decimal places, if needed.)

(a) The distribution of IQ
is approximately normal
.

(b) The distribution of the sample mean IQ is
approximately normal
with a mean of
and a standard deviation of
.

(c) The probability that the sample mean IQ is less than 116 is
.

(d) The probability that the sample mean IQ is greater than 116 is
.

(e) The probability that the sample mean IQ is between 116 and 125 is

Answer 1

(a) The distribution of IQ is approximately normal.

- This statement is already simple and straightforward, indicating that IQ scores are assumed to follow a normal distribution.

(b) The distribution of the sample mean IQ is approximately normal

- This statement is also simple, providing the mean and standard deviation of the sample mean IQ.

(c) The probability that the sample mean IQ is less than 116 is approximately 0.0899.

(d) The probability that the sample mean IQ is greater than 116 is approximately 0.9101.

(e) The probability that the sample mean IQ is between 116 and 125 is approximately 0.8632.