Question

The age of professional racecar drivers is normally distributed with a mean of 39 and a standard deviation of 8. One driver is randomly selected. 95% of all drivers are younger than what age?

Answer 1

To find the age at which 95% of all drivers are younger, we can use the z-score formula to find the corresponding z-score and then convert it back to the original measurement using the mean and standard deviation.

Step-by-step explanation:

To find the age at which 95% of all drivers are younger, we need to find the z-score corresponding to the 95th percentile of the standard normal distribution. The z-score can be found using the z-score formula: z = (x - mean) / standard deviation. Substituting the given values, we have: z = (x - 39) / 8. To find the value of x, we can rearrange the formula: x = (z * standard deviation) + mean = (1.645 * 8) + 39 = 13.16 + 39 = 52.16. Therefore, 95% of all drivers are younger than 52.16 years old.