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?A 0.1894 B 0.3106C 0.8106D 0.8800
Accepted Solution
A:
Answer: C. 0.80920Step-by-step explanation: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