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.)
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
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 0.81 inch? (Give the answer to four decimal places.)
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 that value. Here's how you can do it:
Step 1: Standardize the value
To standardize the value 0.83 inch, we'll subtract the mean from it and divide by the standard deviation:
z = (0.83 - 0.8) / 0.01
z = 0.03 / 0.01
z = 3
Step 2: Find the probability using a z-table or calculator
Now, we need to find the cumulative probability associated with a z-value of 3. We can use a z-table or a calculator to find this value.
Using a calculator, you can use the "cumulative distribution function" (CDF) of the normal distribution. By entering a z-value of 3 into the CDF function, it will give you the probability that a randomly selected value from the distribution is less than or equal to that value. To find the probability that the diameter will exceed 0.83 inch, we can subtract the CDF value from 1.
Using a z-table, locate the row for 3.0 in the z-table and find the corresponding column for the tenth decimal place (0.0). The value in that cell represents the probability to the left of the z-value. To find the probability to the right of the z-value, subtract that value from 1.
After these calculations, you will get the probability that the diameter will exceed 0.83 inch. Make sure to round the answer to four decimal places as instructed in the question.