Question

Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 47 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

To calculate the probability of a random person on the street having an IQ score of less than 98, we need to use the normal distribution and the given mean (μ) and standard deviation (σ).

The probability can be found by calculating the z-score for an IQ score of 98 and then using a standard normal distribution table or calculator to find the corresponding probability.

The formula to calculate the z-score is:

z = (X - μ) / σ

Where:

X = IQ score (98)

μ = mean (100.0)

σ = standard deviation (15.0)

Let's calculate the z-score:

z = (98 - 100.0) / 15.0

z = -0.1333

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.1333.

The probability of a random person on the street having an IQ score of less than 98 is approximately 0.4478 (rounded to 4 decimal places).

Therefore, the probability is 0.4478.