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?
A)0.0596
B)0.9332
C)0.4332
D)0.0668

Question

Quizplus · Accepted Answer

To find the probability that the diameter of a randomly selected pencil will be less than 0.285 inches, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Plugging in the values: Z = (0.285 - 0.30) / 0.01 = -1.5. Looking up the Z-score of -1.5 in a standard normal distribution table gives a probability of approximately 0.0668.

The Diameters of Pencils Produced by a Certain Machine Are