Exhibit 6-1.You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough.The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. Refer to Exhibit 6-1.Above what temperature must the sleeping bag be suited such that the temperature will be too cold only 5% of the time?

Question

Quizplus · Accepted Answer

We need to find the cutoff temperature above which the temperature will be too cold only 5% of the time. This can be found using the standard normal distribution table or calculator.

First, we calculate the z-score corresponding to the 5th percentile:

z = invNorm(0.05) = -1.645

Then we use the z-score formula to solve for the corresponding temperature:

z = (x - mu) / sigma

-1.645 = (x - 32) / 8

x = -1.645 * 8 + 32 = 18.84

Therefore, the sleeping bag must be suited for temperatures above 18.84°F such that the temperature will be too cold only 5% of the time.