2 0/3 points I Previous Answers PODStat5 7.E.095. My Notes Suppose that the dist

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2 0/3 points I Previous Answers PODStat5 7.E.095. My Notes Suppose that the distribution of x = the number of items produced by an assembly line during an 8-hour shift can be approximated by a normal distribution with mean value 160 and standard deviation 10. (Round your answers to four decimal places.) (a) What is the approximate probability that the number of items produced is at most 130? P(x s 130)- (b) What is the approximate probability that at least 140 items are produced? P(x2140)= .4773 (c) What is the approximate probability that between 145 and 170 (inclusive) items are produced? (145 x 170) = You may need to use the appropriate table in Appendix A to answer this question Need Help? Read ItTalk to a Tutor

Explanation / Answer

Mean is 160 and s is 10

z is given as (x-mean)/s

a) P(x<130)=P(z<(130-160)/10)=P(z<-3) or 1-P(z<3), from normal distribution table we get 1-0.9987=0.0013

b) P(x>140)=P(z>(140-160)/10) =P(z>-2) or P(z<2) which is 0.9772

c) P(145<x<170)=P((145-160)/10<z<(170-160)/10)=P(-1.5<z<1) or P(z<1)-P(z<-1.5) or P(z<1)-(1-P(z<1.5))

from normal table it is 0.8413-(1-0.9332)=0.7745

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