Question

A southwestern tourist city has records indicating that the average daily temperature in summer is 82 degrees F, which is normally distributed with a standard deviation of 3 degrees F. Based on these records, determine: A) The probability of a daily temperature between 79 degrees F and 85 degrees F B) The probability that the daily temperature exceeds 92 degrees F C) The probability that the daily temperature will is below 73 degrees F

Answer 1

This is a normal distribution question with

a) x1 = 79
x2 = 85
P(79.0 < x < 85.0)=?

This implies that
P(79.0 < x < 85.0) = P(-1.0 < z < 1.0) = 0.6826
b) x = 92
P(x > 92.0)=?

z = 3.3333
This implies that
P(x > 92.0) = P(z > 3.3333) = 0.0004
c) x = 73
P(x < 73.0)=?

z = -3.0
This implies that
P(x < 73.0) = P(z < -3.0) = 0.0013
PS: you have to refer z score table to find the final probabilities.
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