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?

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ethan2020298 ethan2020298 · Answer 1 · 2016-04-14T03:07:03+02:00

It would be more odd in Honolulu.

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slicergiza slicergiza · Answer 2 · 2019-06-21T09:19:37+02:00

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,

[tex]\mu_1[/tex] = 21° F,

Having standard deviation,

[tex]\sigma_1[/tex] = 10°,

Thus, the z-score for the high temperature of 57° F in alaska,

[tex]z_1=\frac{57-\mu_1}{\sigma_1}[/tex]

[tex]=\frac{57-21}{10}[/tex]

[tex]=3.6[/tex]

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,

[tex]\mu_2=80^{\circ}[/tex]

Having standard deviation,

[tex]\sigma_2=8^{\circ}[/tex]

Thus, the z-score for the high temperature of 57° F in Honolulu,

[tex]z_2=\frac{57-\mu_2}{\sigma_2}[/tex]

[tex]=\frac{57-80}{8}[/tex]

[tex]=-2.875[/tex]

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.