The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285 inches?

Answer:the probability that the diameter of a randomly selected pencil will be less than 0.285 inches is 0.06681

Step-by-step explanation:

Since the diameters of pencils produced by a certain machine are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u) / s

Where

x = diameters of pencils produced by a certain machine

u = mean diameter

s = standard deviation

From the information given,

u = 0.30 inches

s = 0.01 inches

We want to find the probability that the diameter of a randomly selected pencil will be less than 0.285 inches. It is expressed as

P (x lesser than 0.285)

For x = 0.285

z = (0.285 - 0.3) / 0.01 = - 1.5

Looking at the normal distribution table, the corresponding z score is

0.06681