An automatic machine in a manufacturing process is operating properly if the len
ID: 3265437 • Letter: A
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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