Question

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 80 inches and a standard deviation of 15 inches. What is the probability that the annual snowfall during one randomly selected year will be more than 75 inches?

1. Less than 25%
2. Between 25% and 50%
3. Between 50% and 75%
4. More than 75%

Answer 1

To find the probability that the annual snowfall during one randomly selected year will be more than 75 inches, use the z-score formula to find the probability of a z-score less than -0.333, and subtract this from 1.

Step-by-step explanation:

To find the probability that the annual snowfall during one randomly selected year will be more than 75 inches, we can use the z-score formula. The z-score is found by subtracting the mean from the value and dividing by the standard deviation: z = (75 - 80) / 15 = -0.333. We then use a z-table or calculator to find the probability that a z-score is less than -0.333.

From the table, we find this probability to be approximately 0.3686. However, we want the probability that the snowfall is more than 75 inches, so we subtract this probability from 1: 1 - 0.3686 = 0.6314. Therefore, the probability that the annual snowfall will be more than 75 inches is approximately 0.6314 or 63.14%.