The diameter of an electric cable is normally distributed, with a mean of 0.6 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.61 inch?
plug in your data at
http://davidmlane.com/hyperstat/z_table.html
It is an excellent tool
To find the probability that the diameter of an electric cable will exceed 0.61 inch, we can use the z-score formula and the standard normal distribution.
The z-score formula is given by:
z = (x - μ) / σ
Where:
x is the given value (0.61 inch in this case)
μ is the mean of the distribution (0.6 inch in this case)
σ is the standard deviation of the distribution (0.01 inch in this case)
First, we calculate the z-score:
z = (0.61 - 0.6) / 0.01
z = 0.01 / 0.01
z = 1
Next, we use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1. This probability represents the area under the standard normal distribution curve to the right of the z-score.
Using the table or calculator, we find that the probability associated with a z-score of 1 is approximately 0.8413.
Therefore, the probability that the diameter will exceed 0.61 inch is approximately 0.8413 or 84.13%.