The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is between 95 and 105?
A)0.0182
B)0.9818
C)1.00
D)Very unlikely

Question

Quizplus · Accepted Answer

We can use the formula for the standard error of the mean:

standard error of the mean = standard deviation / square root of sample size

= 15 / sqrt(50)

= 2.1213

We can then calculate the z-score for each of the two values we are interested in:

z1 = (95 - 100) / 2.1213 = -2.36
z2 = (105 - 100) / 2.1213 = 2.36

Using a standard normal distribution table, we can find the area to the left of z1 and z2:

area to the left of z1 = 0.0099
area to the left of z2 = 0.9901

The probability of getting a sample mean between 95 and 105 is the area between z1 and z2, which is:

prob = area to the left of z2 - area to the left of z1
= 0.9901 - 0.0099
= 0.9802

Therefore, the probability of getting a sample mean between 95 and 105 is 0.9802, which is approximately 0.9818. The best choice is B, which is the closest answer to this value.

The Intelligence Quotient (IQ)test Scores for Adults Are Normally Distributed