Question

Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 43 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

Using the normal distribution, it is found that there is a 0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Normal Probability Distribution

In a normal distribution with mean  and standard deviation, the z-score of a measure X is given by:

$Z=\dfrac{x-\mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.
• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are, respectively, given by and.

The probability of a random person on the street having an IQ score of less than 98 is the p-value of Z when X = 98, hence:

$Z=\dfrac{x-\mu}{\sigma}$

$Z=\dfrac{98-100}{15}$

$Z=-0.13$

Has a p-value of 0.4483.

0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.

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