Please help with difficult stats question?

Question

The weights of domestic, adult cats are normally distributed with a mean of 10.42 pounds and a standard deviation of 0.87 pounds.
A cat food manufacturer sells three types of foods for underweight, normal, and overweight cats. The manufacturer considers the bottom 5% of cats underweight and the top 10% overweight. Compute what weight range must be specified for each of the three categories.
Underweight:
Normal:
Overweight:
I am having trouble with this one--it has to be formatted to 8 decimal places using excel. The function for this is NORMINV from the stats menu--but I cannot comeup with any numbers--I keep getting an error message!

Answer 1

Gosh. I have no idea how to do it in excel....

but for a normal distribution with an error function that always returns 1 (no error) then the percentage of the population between -n standard deviations and +n standard deviations is n/(sqrt(2)

So, if you want there to be 90% of the population between -n and +n so that 5% is below -n and 5% is above +n then

0.9 = n/sqrt(2)
0.9 * sqrt(2) = n

1.27279221 = n

so, now we take 1.27279221 time the standard deviation of 0.87 and then subtract it from 10.42

Underweight = 10.42 - (1.27279921 * 0.87)

= 9.31266469

and then you do the same thing for 80% (except you add) to get the weight at 10% over....

Answer 2

It really sounds like you're having a problem with Excel, not the stat, right?

Look up the Z values for 5% an 90% from the standard tables. Then, since you have the mean and the SD you can get values for weight.

That's all you want, right?

You might post in the computer questions for help with the excel.

Answer 3

You just need to compute the z scores for the other 2 officers z = (x - mean) / std dev Officer A: (72 - 76) / 12 = - .3333... Officer B: (74 - 76) / 12 = - .1666... Officer C: z = .50 This is the lowest-to-highest order