Some people claim that climate change is already affecting the amounts of precip

Question

Some people claim that climate change is already affecting the amounts of precipitation that certain areas will get. Indeed, the last ten years worth if rainfall data in Los Angeles appears to support that claim, since the average April rainfall over those years is 5.97 inches, which is higher than the other data suggets. Mean= 4.004 Standard deviation= 2.26

a) assuming that the mean and standard deviation have not chnaged, find the probability of selecting 10 years with an average of 5.97 inches or more in april. Explain

b) Is a ten-year avaerage of 5.97 inches (or more) in A pril unusual? Explain

Explanation / Answer

a) here for n=10 years ; std error of mean =std deviation/(n)1/2 =2.26/(10)1/2 =0.715

therefore  probability of selecting 10 years with an average of 5.97 inches or more in april.=P(X>5.97)

=1-P(X<5.97)=1-P(Z<(5.97-4.004)/0.715)=1-P(Z<2.7509)=1-0.9970=0.0030

b) as above probability is less then 0.05 level; therefore  ten-year avaerage of 5.97 inches (or more) in A pril is unusual.

please revert for any clarification required.

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