The diameter of an electric cable is normally distributed, with a mean of 0.6 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.62 inch? (You may need to use the standard normal distribution table.
To find the probability that the diameter will exceed 0.62 inch, we can use the standard normal distribution table, also known as the Z-table.
First, we need to calculate the Z-score for the given value of 0.62 inch. The Z-score is calculated using the formula:
Z = (X - μ) / σ
where X is the value, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
Z = (0.62 - 0.6) / 0.02
= 0.02 / 0.02
= 1
Now, we can use the Z-table to find the probability corresponding to a Z-score of 1.
The Z-table provides the area under the standard normal curve up to a given Z-score. Since we are interested in the probability that the diameter exceeds 0.62 inch, we need to find the area to the right of the Z-score of 1.
Looking up the Z-score of 1 in the Z-table, we find that the corresponding area is 0.8413.
However, this is the area to the left of 1, and we need the area to the right. To find this, we subtract the given area from 1:
Area to the right = 1 - 0.8413
= 0.1587
Therefore, the probability that the diameter will exceed 0.62 inch is approximately 0.1587 or 15.87%.
http://davidmlane.com/hyperstat/z_table.html
here
z = (.62 - .60) / .02 = 1