Question

The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. If X` represents the average amount of snowfall in 5 years, find k such that P(X`<k)=0.85. Round your answer to 3 decimal places.

Group of answer choices

80.364

65.365

46.825

74.635

93.175

Answer 1

Solution:

Given that,

mean = = 70

standard deviation = = 10

n = 5

=10

₌ / n = 10 5 = 4.4721

Using standard normal table,

P(Z < z) = 0.85

P(Z <1.036) = 0.85

z = 1.036

Using z-score formula,

x = z * +

x = 1.036 *4.4721+ 70

x = 74.635