Annual Precipitation The average annual precipitation. for a large Midwest city

Question

Annual Precipitation The average annual precipitation. for a large Midwest city is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed. a. Find the probability that a randomly selected month will have less than 30 inches. 0.4052 or 40.52% TI: 0.4067) b. Find the probability that the mean of a random selection of 32 months will have a mean less than 30 inches, 0.0901 or 9.01% (TI 0.0908) c. Does it seem reasonable that one month could have a rainfall amount less than 30 inches? Yes, the probability is slightly more than 40% d. Does it seem reasonable that the mean of a sample of 32 could be less than 30 inches? It's possible since the probability is about 9% Systolic Blood Pressure Assume that the mean systolic blood pressure of normal adults is 120 millimeters of

Explanation / Answer

Mean ( u ) =30.85
Standard Deviation ( sd )=3.6
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X < 30) = (30-30.85)/3.6
= -0.85/3.6= -0.2361
= P ( Z <-0.2361) From Standard Normal Table
= 0.4052
b.
P(X < 30) = (30-30.85)/3.6/ Sqrt ( 32 )
= -0.85/0.6364= -1.3356
= P ( Z <-1.3356) From Standard NOrmal Table
= 0.0908                  
c.
yes since it has the probability as 0.4052 which is more than 40%              
d.
it can be since the probability is slight less than, < 0.10

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