Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca

FizeauV

FizeauV

Answered question

2021-10-13

Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. 1) During what percentage of years does Ithaca get more than 40" of rain? 2) Less than how much rain falls in the driest 20% of all years? 3) A Cornell University student is in Ithaca for 4 years. Let y represent the mean amount of rain for those 4 years. Describe the sampling distribution model of this sample mean, y. 4) What 's the probability that those 4 years average less than 30" of rain?

Answer & Explanation

gotovub

gotovub

Skilled2021-10-14Added 98 answers

Step 1 
(1)μ=35.4 
σ=4.2 
P(40X)=P(4035.44.2z)=P(1.095z) 
P(1.095z)=0.1368 
Hence during 13.68% percentage of years does Ithaca get more than 40" of rain. 
Step 2 
(2)P(Zz)=0.2 
By Z-table: z=0.84 
x35.44.2=0.84 
x=31.87 
Hence the driest 20% of days there will be approximately 31.87" of rain. 
Step 3 
(3) The shape of the sampling distribution model of the sample mean will be normal distribution. 
μ=35.4 
σ=4.24=2.1 
Step 4 
(4)P(X<30)=P(z<3035.42.1)=P(z<2.57)=0.00506 
Therefore, probability that those 4 year average less than 30" of rain is 0.00506 
Result 
(1) 13.68% 
(2)31.87" 
(3)Normal, Mean 35.4, Standard deviation 2.1   
(4) 0.00506

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