An automatic machine in a manufacturing process is operating properly if the len

Question

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 114 cm and a standard deviation of 4.7 cm

. A. Find the probability that one selected subcomponent is longer than 116 cm. Probability =

B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 116 cm. Probability =

C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 116 cm

Explanation / Answer

a. P(x > 116) = 1 - P(x <116)

                       = 1 - z((116-114)/4.7)

                        = 1 - z(0.4255)

                          = 1 -0.664764

                          = 0.3352

b. P4(x > 116) = 1- P4(z < 116

                       = 1 - z((116 -114)/(4.7/4))

                       = 1 - z(0.8511)

                       = 1 - 0.802643

                        = 0.1974

c.the probability that if 4 are randomly selected, all 4 have lengths that exceed 116 cm = (answer of part a)4

                                                                                                                                        = 0.3352^2

                                                                                                                                        =0.1124

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