Question

Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0

and σ=15.0
. A random sample of 41
people is taken.
Step 1 of 2 : What is the probability of a random person on the street having an IQ score of less than 98
? Round your answer to 4
decimal places, if necessary.

Answer 1

Explanation:

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

z = (x - μ) / σ

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

So, for x = 98, we have:

z = (98 - 100) / 15 = -0.1333

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -0.1333 is approximately 0.4483.

Therefore, the probability of a random person on the street having an IQ score of less than 98 is 0.4483 (or 44.83% rounded to four decimal places).