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 0.83 inch? (Give the answer to four decimal places.)
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To find the probability that the diameter will exceed 0.83 inch, we need to calculate the area under the normal distribution curve to the right of 0.83 inch.
First, we need to standardize the value of 0.83 inch using the formula for standardization:
z = (x - μ) / σ
where x is the value we want to standardize (0.83 inch), μ is the mean (0.8 inch), and σ is the standard deviation (0.01 inch).
Substituting the given values into the formula, we get:
z = (0.83 - 0.8) / 0.01
z = 0.03 / 0.01
z = 3
Now we need to find the probability associated with the z-value of 3. We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table, we find that the probability associated with a z-value of 3 is approximately 0.9987.
Therefore, the probability that the diameter will exceed 0.83 inch is approximately 0.9987 (or 99.87% when converted to a percentage), to four decimal places.