Question

Suppose that the amount of snowfall per storm in Lincoln is normally distributed with µ = 4.2 inches and standard deviation µ = 2.3 inches (totally made up data). If the mayor decides that only the top 5% of storms should have school cancelled, what is the cutoff snowfall for school to be cancelled?

Answer 1

hopes this photo helps

Answer 2

7.9835

Explanation:

Given that :

Mean snowfall per storm (µ) = 4.2 inches standard deviation (s) = 2.3 inches

Only the top 5% of storm should result in school being canceled :

Cut off snowfall for school to be canceled '

P(Z ≥ 5%) ; p(Z ≥ 0.05) = 1.645

Using the z relation :

Z = (x - m) / s

1.645 = (x - 4.2) /2.3

x - 4.2 = 2.3 * 1.645

x - 4.2 = 3.7835

x = 3.7835 + 4.2

x = 7.9835

Cut off snowfall for school to be canceled 7.9835