To find the probability of a random person on the street having an IQ score of less than 99, we need to calculate the area under the normal distribution curve to the left of 99.
Using the given information that IQ scores are normally distributed with a mean (μ) of 100.0 and a standard deviation (σ) of 15.0, we can standardize the value of 99 using the z-score formula:
z = (x - μ) / σ
where x is the value we want to standardize (99 in this case).
Substituting the values, we get:
z = (99 - 100.0) / 15.0
z = -0.0667
Next, we need to find the probability corresponding to this z-score. We can look up this probability in the standard normal distribution table or use statistical software.
The probability of a random person on the street having an IQ score of less than 99 is approximately 0.4744 (rounded to 4 decimal places).
Therefore, the probability is 0.4744.