7) Suppose the weights of college textbooks are normally distributed with a popu

Question

7) Suppose the weights of college textbooks are normally distributed with a population mean of 4 pounds and a population standard deviation of 1.2 pounds. Suppose randomly sample and weigh 16 textbooks. Answer the following questions: What is the probability that the sample average of the 16 textbooks is less than 3.5 pounds? (use 2 decimal places in your answer) a) b) What is the probability that a given (i.e. one) textbook weighs more than 5.5 pounds? (use 2 decimal places in your answer) c) Imagine the distribution of all possible samples averages of textbook weights (with n=16). What is the weight that separates the lightest 25% of sample averages from the heaviest 75% of sample averages? (round your answer to the nearest tenth of a pound)

Explanation / Answer

=4

=1.2

n=16

a)

x=3.5

z=(x-)/(/n)

=(3.5-4)/(1.2/16)

=-0.5/0.3

=-1.67

P(x<3.5) =P(z<-1.67)

               =0.0475

b)

x=5.5

n=1

z=(x-)/(/n)

=(5.5-4)/(1.2/1)

=1.5/1.2

=1.25

P(x>5.5) =P(z>1.25)

               =1-P(z<1.25)

               =1-0.8944

               =0.1056

c)

For P=25% =0.25, the z score is -0.67

So

x=z*(/n) +

=-0.67(1.2/16) +4

=-0.67*0.3 +4

=-0.201 +4

=3.799

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