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

Given : The average low temperature in the park for May follows a normal distribution with a mean of [tex]\mu=32^{\circ}F[/tex] and a standard deviation of [tex]s=8^{\circ}F[/tex].

Let x represents the temperature in the park for May .

Using formula : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 25

[tex]z=\dfrac{25-32}{8}=-0.875[/tex]

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

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