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Chapter 2: Q T2.5. (page 149)

The average yearly snowfall in Chilly Ville is approximately Normally distributed with a mean of 55 inches. If the snowfall in Chilly Ville exceeds 60 inches in 15% of the years, what is the standard deviation?

a. 4.83 inches

b. 5.18 inches

c. 6.04 inches

d. 8.93 inches

e. The standard deviation cannot be computed from the given information.

Short Answer

Expert verified

The correct option is (a) 4.83inches

Step by step solution

01

Given information

渭=55蟽=60

02

Concept

The formula used:

z=x鈭�渭蟽

03

Calculation

The probability of the snowfall X exceeding 60 inches is 15%

P(X>60)=15%=0.15

So the probability that X does not exceed 60 is

P(X鈮�60)=1鈭�P(X>60)=1鈭�0.15=0.85

The column contains the corresponding 100th of thez-score (0.05) and the raw contains the proper integer 10th of thez-score (0.80), therefore the z-score is

Z=1.04

z=x鈭�渭蟽z蟽=x鈭�渭蟽=x鈭�渭z蟽=60鈭�551.04=4.8077

As a result, the standard deviation is 4.8077 inches, which is quite near to 4.83 inches.

Hence, the correct option is (a)

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