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
