Suppose that the diameter of an electric cable is normally distributed, with a mean of 0.85 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 be greater than 0.84 inches? Please round the answer to the nearest thousandth, if necessary.
A) 0.5
B) 0.159
C) 0.023
D) 0.841
E) 0.977

Question

Quizplus · Accepted Answer

To find the probability that the diameter will be greater than 0.84 inches, we first calculate the z-score for 0.84 inches using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the values, we get $z = \frac{(0.84 - 0.85)}{0.01} = -1$. Looking up the z-score of -1 in the standard normal distribution table or using a calculator, we find that the area to the left of this z-score is approximately 0.159. Since we are interested in the probability of the diameter being greater than 0.84 inches, we subtract this value from 1, resulting in $1 - 0.159 = 0.841$. This means there is an 84.1% chance that the diameter will be greater than 0.84 inches.

Suppose That the Diameter of an Electric Cable Is Normally