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
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
1 answer