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. An inexpensive bag you are considering advertises to be good for temperatures down to

Question

38°F. What is the probability that the bag will not be warm enough?
0.2266
0.7734
0.2734
0.7500

Answer 1

To find the probability that the bag will not be warm enough, we need to calculate the probability of the average low temperature being below 38°F.

First, we convert the average low temperature of 38°F to a standard score (z-score) using the formula:

z = (x - μ) / σ

Where:
x = temperature in question (38°F)
μ = mean (32°F)
σ = standard deviation (8°F)

z = (38 - 32) / 8
z = 6 / 8
z = 0.75

Next, we need to find the probability associated with a z-score of -0.75 using a standard normal distribution table or calculator. The probability is the area to the left of the z-score.

Looking up -0.75 in a standard normal distribution table, we find that the probability is approximately 0.2266.

Therefore, the probability that the bag will not be warm enough is 0.2266.