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. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park?

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize the value of 25°F using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

z = (25 - 32) / 8 = -0.875

We then look up the probability of z being less than or equal to -0.875 in a standard normal distribution table or by using a calculator.

Using a calculator, we find that P(z ≤ -0.875) = 0.1894.

Since the probability of the temperature being lower than 25°F is only 0.1894, the probability of the sleeping bag being warm enough is 1 - 0.1894 = 0.8106 or approximately 0.81.

Therefore, the best choice is C, with a probability of 0.8092.

You Are Planning a May Camping Trip to Denali National