The diameter of an electric cable is normally distributed, with a mean of 0.8 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.82 inch? (Give the answer to four decimal places.)

Use same process as indicated in your later post.

To find the probability that the diameter will exceed 0.82 inch, we need to calculate the area under the normal distribution curve to the right of 0.82 inch.

First, we need to standardize the value 0.82 inch using the formula for standardization:

Z = (X - μ) / σ

Where:
X = 0.82 (the value we want to find the probability for)
μ = 0.8 (mean of the distribution)
σ = 0.01 (standard deviation of the distribution)

Substituting the values into the formula:

Z = (0.82 - 0.8) / 0.01
Z = 0.02 / 0.01
Z = 2

Next, we need to find the probability corresponding to a Z-value of 2. To do this, we can refer to a standard normal distribution table or use a statistical software or calculator.

Using a standard normal distribution table, we can find the probability associated with a Z-value of 2. In the table, the area to the left of 2 is 0.9772. Since we want the probability to the right of 0.82 inch, we subtract this value from 1:

P(Z > 2) = 1 - 0.9772 = 0.0228

So, the probability that the diameter will exceed 0.82 inch is approximately 0.0228 (rounded to four decimal places).