Question

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?

Multiple Choice
A. 18940.
B. 31060.
C. 80920.
D. 8800

Answer 1

Answer: C. 0.80920

Explanation:

Given : The average low temperature in the park for May follows a normal distribution with a mean of
`\mu=32^(\circ)F` and a standard deviation of
`s=8^(\circ)F`.

Let x represents the temperature in the park for May .

Using formula :
`z=(x-\mu)/(\sigma)`

For x= 25

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

Then by using the standard z-table for right tail test,
`P(x>25)=P(z>-0.875)\\\\=1-P(z>0.875)\\\\=1-0.1908=0.80920`

Hence, the probability that this bag will be warm enough on a randomly selected May night at the park= 0.80920