Find the two weights that seperate the top 3% and bottom 3%.?

Question

The weights of certain machine component are normally distributed with the mean of 8.92g and a standard deviation of 0.06g.

Answer 1

after you plug the mean and sd into the normal distribution function, set up the equation (integral of function from some point m out to infinity = .03 and solve for m) That gives you the top 3 percent. Then finding the other cutoff shouldn't be a problem.

Answer 2

zagwask is misleading.

These probabilities are tabulated in the standard normal table.

For the bottom, look in your table and find Zc such that

P(z
Then unwind this Zc

Zc = (wt-mean)/sd , you know mean and sd, and Zc -> wt
This should give you a weight about 2 sd below the mean.

Now for the upper 3%, the distribution is symmeterical, and so the area of the right tail is the same as the left tail

This means that you use Zc but make it positive and solve for wt.

The difference between the mean and the low weight should be equal to the difference between the high weight and the mean. this is what symmetry means.

Post you solutions, and someone will check them for you.