The average high temperature in Anchorage, Alaska, in January is 21°F with a standard deviation of 10°. The average high temperature in Honolulu in January is 80°F with a standard deviation of 8°. In which location would it be more unusual to have a day in January with a high of 57°F?
Answer:
In Honolulu it be more unusual to have a day in January with a high of 57°F
Step-by-step explanation:
Given,
The average high temperature in Anchorage, Alaska,
\(\mu_1\) = 21° F,
Having standard deviation,
\(\sigma_1\) = 10°,
Thus, the z-score for the high temperature of 57° F in alaska,
\(z_1=\frac{57-\mu_1}{\sigma_1}\)
\(=\frac{57-21}{10}\)
\(=3.6\)
By the z-score table the probability of the high temperature of 57°F in Alaska = 0.99984 = 99.984 %
Now, the average high temperature in Honolulu is,
\(\mu_2=80^{\circ}\)
Having standard deviation,
\(\sigma_2=8^{\circ}\)
Thus, the z-score for the high temperature of 57° F in Honolulu,
\(z_2=\frac{57-\mu_2}{\sigma_2}\)
\(=\frac{57-80}{8}\)
\(=-2.875\)
By the z-score table the probability of the high temperature of 57° in Honolulu = 0.00205 = 0.205 %
Since, a probability is unusual if it is less than 5 %,
Hence, In Honolulu it be more unusual to have a day in January with a high of 57°F.