Find the indicated probability.
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?
(1 point)
Responses
0.0596
0.0668
0.4332
0.9332
To find this probability, we first need to standardize the value 0.285 inches using the z-score formula: z = (X - μ) / σ
z = (0.285 - 0.30) / 0.01
z = -0.015 / 0.01
z = -1.5
Next, we can use a standard normal distribution table or a calculator to find the probability that a z-score of -1.5 corresponds to:
P(Z < -1.5) ≈ 0.0668
Therefore, the probability that the diameter of a randomly selected pencil will be less than 0.285 inches is approximately 0.0668.
The correct response is: 0.0668