Question

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 1

It would be more odd in Honolulu.

Answer 2

In Honolulu it be more unusual to have a day in January with a high of 57°F

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=(57-\mu_1)/(\sigma_1)`

`=(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=(57-\mu_2)/(\sigma_2)`

`=(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.