Question

Assume that adults have IQ scores that are normally distributed with a mean of

μ=105 and a standard deviation of σ=15. Find the probability that a randomly selected adult has an IQ between 95 and 115.

Answer 1

To solve this problem, we need to standardize the IQ scores using the z-score formula:

z = (x - μ) / σ

where x is the IQ score, μ is the mean IQ, and σ is the standard deviation.

For x = 95, we have:

z = (95 - 105) / 15 = -0.67

For x = 115, we have:

z = (115 - 105) / 15 = 0.67

Now, we can use a standard normal table or a calculator to find the probability that a z-score is between -0.67 and 0.67. Using a standard normal table, we find:

P(-0.67 < z < 0.67) = 0.4978

Therefore, the probability that a randomly selected adult has an IQ between 95 and 115 is 0.4978 or about 49.78%.