Question

Annual snowfall in Anchorage, Alaska, is normally distributed with a mean height of 76 inches and a standard deviation of 4.7 inches. What is the probability this year that it will snow between 71.4 and 80.7 inches in Anchorage? 67.75% 54.71% 38.14% 23.22%

Answer 1

67.75%

Explanation:

Given:

Given that:

µ = 76 ; σ = 4.7

P(x < 80.7) - P(x < 71.4)

Obtain the standardized score, Z ; x = 71. 4

Zscore = (x - μ) / σ

P(x < 71.4) = (71.4 - 76) / 4.7

P(x < 71.4) = - 4.6 / 4.7

P(x < 71.4) = - 0.9787

P(z < 0.9787) = 0.16386

x = 80.7

P(x < 80.7) = (80.7 - 76) / 4.7

P(x < 80.7) = 4.7 / 4.7

P(x < 80.7) = 1

P(z < 1) = 0.84134

0.84134 - 0.16386 = 0.67748 = 67.748% = 67.75%