Do your work neatly In the blue book. You are allowed 3 sheets of blank scrap pa

Question

Do your work neatly In the blue book. You are allowed 3 sheets of blank scrap paper. When you are finished your exam, return all papers, the test paper, your scrap papers and your blue book. Talking to another student will cancel your exam. No sharing of calculators or anything. The heights of men at a gym are normally distributed with mu = 70in and sigma = 3in At a gathering of 280 college students their grade-group and major were recorded as follows: If a student is selected at random from this group, find the probability that the student is:

Explanation / Answer

Mean ( u ) =70
Standard Deviation ( sd )=3
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 63) = (63-70)/3
= -7/3 = -2.3333
= P ( Z <-2.3333) From Standard Normal Table
= 0.00982
P(X < 70) = (70-70)/3
= 0/3 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(63 < X < 70) = 0.5-0.00982 = 0.4902  
b.
P(X < 67) = (67-70)/3
= -3/3= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587                  
c.
P(X > 74) = (74-70)/3
= 4/3 = 1.3333
= P ( Z >1.333) From Standard Normal Table
= 0.0912                  
              

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