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