Suppose that the distribution of the number of items x produced by an assembly l

Question

Suppose that the distribution of the number of items x produced by an assembly line during an 8-hr shift can be approximated by a normal distribution with mean value 150 and standard deviation 10. (Round your answers to four decimal places.)

(a) What is the probability that the number of items produced is at most 130?
P(x 130) =   

(b) What is the probability that at least 130 items are produced?
P(x 130) =   

(c) What is the probability that between 135 and 159 (inclusive) items are produced?
P(135 x 159) =

Explanation / Answer

Mean is 150 and sd is 10

a) P(x<130)=P(z<(130-150)/10)= P(z<-2)=1-P(z<2). From the normal distribution table we get 1-0.9772=0.0228

b) P(x>130)=1-P(x<130)=1-0.0228=0.9772

c) P(135 x 159) = P((135-150)/10<Z<(159-150)/10)=P(-1.5<Z<0.9) =P(Z<0.9)-(1-P(Z<1.5))

From normal distribution table we get 0.8158-(1-0.9332)=0.749

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