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