Temperatures in June in LA are distributed nearly normally with mean 77 degrees and standard deviation 5 degrees F. In what proportion of days in June in LA is the temperature over 85 degrees?

Question

Social Studies

Camron

29 April, 17:44

Temperatures in June in LA are distributed nearly normally with mean 77 degrees and standard deviation 5 degrees F. In what proportion of days in June in LA is the temperature over 85 degrees?

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Answers (1)

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Cailyn Weber · Answer 1

5.5%

Explanation:

Given

μ = 77 degrees

σ = 5 degrees

X = 85 degrees

First, we need to calculate the z-score

Z = (X-μ) / σ

Z = (85-77) / 5 = 1.60

Then, we need to refer to the normal probability table, locate 1.6 on the row and 0.00 on the column. And a Z-score of 1. 6 then corresponds to the value at the intersection, which is 0.9452.

Remember, the Z-score refer to the area under the curve below observation value, so to find the area above the curve below the observation value, we simply need to find the complement, which is 1 - 0.9452 = 0.0548, roughly the 5.5%.