Question
Asked Nov 9, 2019
Solve the problem.
13) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches,
and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25
randomly picked years will exceed 72.8 inches?
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Solve the problem. 13) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches?

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Step 1

13.

It is mentioned that the amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches.

The sample size of randomly selected years is 25.

 

That is, 700 =10and n = 25
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That is, 700 =10and n = 25

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Step 2

The probability that the mean annual snowfall will exceed 72.8 inches can be obtained as given below:

 

72.8-70
P(>72.8)= P
10
25
2.8
= PZ>
2
- P(Z>1.40)
=1-P(Z <1.40)
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72.8-70 P(>72.8)= P 10 25 2.8 = PZ> 2 - P(Z>1.40) =1-P(Z <1.40)

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Step 3

The probability of Z less than 1.40 can be found by using Excel command = NORM.S.DIST (1.40, TRUE)

The output obtained using ...

f NORM.S.DIST(1.4,TRUE)
A1
B
C
E
F
0.919243
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f NORM.S.DIST(1.4,TRUE) A1 B C E F 0.919243

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