Question

The diameter of an electric cable is normally distributed, with a mean of 0.8 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.82 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.)

Answer 1

Let \(X\) be the diameter of the electric cable. The problem then asks to find \(P(X>0.82)\)

What you can do is standardize \(X\) (get a z-score) and then using the standard normal distribution tale.
\[P(X>0.82)=P\left( \frac{X-0.8}{0.02}>\frac{0.82-0.8}{0.02}\right) =P(Z>1)\]
AT this point, you can use the standard normal table, or remember that between -1 and +1 standard deviations from the mean, the data should encompass around 66.8% of the data. Then use a symmetry argument to find the probability for P(Z>1)

Answer 2

Oops the area under the curve should encompass around 68% of the data**

Answer 3

but if you need an answer with 3 decimal places, your best bet is using the normal table to get more exact values :)

Answer 4

im still confused

Answer 5

do you understand how I got to the \(P(Z>1)\) part?

Answer 6

naw

Answer 7

Well you have \(X\) (the diameter of electrical cable) is normally distributed. But you need to standardize \(X\) so that you can find its probability in a standard normal table.

To standardize \(X\), you do:
\[ Z=\frac{X-\mu}{\sigma}\], where \(\mu\) is the mean, and \(\sigma\) is the standard deviation. The result of that fraction is called \(Z\), which will represent a z-score, and nor has a standard normal distribution. (A standard normal distribution, is the same as the normal distribution except that the mean and standard deviation have been "scaled" to be 0 and 1 respectively).

Answer 8

ummm

Answer 9

Really what you have to do is apply the formula above... \[P(X>0.82)=P\left( \frac{X-0.8}{0.02}>\frac{0.82-0.8}{0.02}\right) =P(Z>1)\]
Since \(\mu = 0.8\) and \(\sigma = 0.02\)

Answer 10

ok