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The annual precipitation amounts in a certain mountain range are normally distributed with a mean of...

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 73 inches, and a standard deviation of 12 inches. What is the probability that the mean annual precipitation during 36 randomly picked years will be less than 75.8 inches?

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = 73

standard deviation = = 12

n = 36

= 73

=  / n = 12/ 36=2

P( < 75.8) = P[( - ) / < (75.8-73) /2 ]

= P(z < 1.4)

Using z table  

= 0.9192   

probability= 0.9192   

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