Suppose that the diameter of an electric cable is normally distributed, with a mean of 0.80 inches and a standard deviation of 0.01 inches. Suppose that a sample of the cable is randomly selected. What is the probability that the diameter will exceed 0.82 inches? Please round the answer to the nearest thousandth, if necessary.
A) 0.159
B) 0.977
C) 0.500
D) 0.841
E) 0.023

Question

Quizplus · Accepted Answer

We need to find the probability that the diameter will exceed 0.82 inches. This can be represented as P(X > 0.82), where X is the diameter of the cable. Using the formula for standardizing a normally distributed variable, we get:

Z = (X - μ) / σ

where μ = 0.80, σ = 0.01, and X = 0.82. Substituting the values, we get:

Z = (0.82 - 0.80) / 0.01 = 2

Now, we need to find the area under the standard normal distribution curve to the right of Z = 2. Using the standard normal distribution table or calculator, we find that the area is approximately 0.0228. Therefore, the probability that the diameter will exceed 0.82 inches is 0.0228 or 0.023 (rounded to the nearest thousandth). Hence, the correct answer is E.

Suppose That the Diameter of an Electric Cable Is Normally