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 140 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 120?
P(x 120) =

(b) What is the probability that at least 120 items are produced?
P(x 120) =

(c) What is the probability that between 125 and 149 (inclusive) items are produced?
P(125 x 149) =

Explanation / Answer

We are given,

Mean = 140

Standard deviation = 10

z = ( x – Mean ) / Standard deviation

Part a

P (x120)

z = (120-140)/10 = 2

P (z2)

By using Normal Distribution Table we get,

P (z2 ) = 0.9772

Answer: 0.9772

Part b

P (x120)

= 1 – P(x<120)

= 1 – 0.9772

= 0.0228

Answer: 0.0228

Part c

P (125 x 149)

z1 = (125-140)/10 = -1.5

z2 = (149-140)/10 = 0.9

P (-1.5 z 0.9)

= P (z0.9) – P (z-1.5)

= 0.8159 – 0.0668

= 0.7491

Answer: 0.7491

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