An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 111 cm and a standard deviation of 5.2 cm. A. Find the probability that one selected subcomponent is longer than 113 cm.

the probability that one selected subcomponent is longer than 113 cm is 0.65

Step-by-step explanation:

if the lengths of an important subcomponent are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = lengths of selected subcomponent.

µ = mean length

σ = standard deviation

From the information given,

µ = 111 cm

σ = 5.2 cm

We want to find the probability that one selected subcomponent is longer than 113 cm. It is expressed as

P(x > 113) = 1 - P(x ≤ 113)

For x = 113,

z = (113 - 111)/5.2 = - 0.38

Looking at the normal distribution table, the probability corresponding to the z score is 0.35

P(x > 113) = 1 - 0.35 = 0.65