1. ## Confidence Levels

A set of metal bars are known to have a mean diameter of 13.03mm with standard deviation of 0.63mm. If it can be assumed that diameters are normally distributed:
i. find the 90% and 95% confidence levels for the diameter of an individual bar.

is this 13.03 +- 1.96(0.63) and 13.03 +- 1.64(0.63) ?

ii. What proportion of the bars will have a diameter greater than 13.75mm?

2. Originally Posted by tone999
A set of metal bars are known to have a mean diameter of 13.03mm with standard deviation of 0.63mm. If it can be assumed that diameters are normally distributed:
i. find the 90% and 95% confidence levels for the diameter of an individual bar.

is this 13.03 +- 1.96(0.63) and 13.03 +- 1.64(0.63) ?
They should be the other way around $\displaystyle 13.03 \pm 1.96(0.63)$ is the $\displaystyle 95\%$ interval and $\displaystyle 13.03 \pm 1.64(0.63)$ the $\displaystyle 90\%$ interval

ii. What proportion of the bars will have a diameter greater than 13.75mm?
The z score for $\displaystyle 13.75$ is:

$\displaystyle z=\frac{13.75-13.03}{0.63}$

which you now look up in the table of the cumulative standard normal distribution and the required probability is $\displaystyle 1-P(z)$.

CB