The diameter of an electric cable is normally distributed, with a mean of 0.7 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.71 inch?
To find the probability that the diameter of an electric cable will exceed 0.71 inch, we need to use the normal distribution and Z-score.
The Z-score measures the number of standard deviations an observation is from the mean. It is calculated using the formula:
Z = (X - μ) / σ
Where:
- Z is the Z-score
- X is the value we want to find the probability for (0.71 inch)
- μ is the mean of the distribution (0.7 inch)
- σ is the standard deviation of the distribution (0.01 inch)
Now we can calculate the Z-score:
Z = (0.71 - 0.7) / 0.01 = 0.01 / 0.01 = 1
The Z-score tells us that the value 0.71 inch is 1 standard deviation above the mean.
To find the probability that the diameter will exceed 0.71 inch, we need to find the area under the standard normal distribution curve that corresponds to Z > 1.
Using a standard normal distribution table or a calculator, we can find the probability associated with Z > 1 as approximately 0.1587.
Therefore, the probability that the diameter of the electric cable will exceed 0.71 inch is approximately 0.1587 or 15.87%.