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.

Answer: 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