How do I find the mean and standard deviation from certain percentages to solve this problem?

Question

This is the problem I'm trying to solve:

A company that sells machines that fills soda cans has claimed that not only will their machine under-fill only 0.5% of cans, but that 90% of cans will have less than 12.1 ounces. What Normal model parameters (mean, standard deviation) is this company claiming? Round to the nearest 0.001.

                                                       N( ______, ______ ) 

I don't know how to approach this question or where to start. Can someone help me solve this problem?

Answer 1

A lot is not said here but left to interpret. My guess is that these are 12-oz cans and underfill means < 12 oz.

Then, we have 1/2 % < 12 and 90% < 12.1

z_.005 = , in Excel, normsinv(.005) = -2.5758293035489

z_.9 = , in Excel, normsinv(.9) = 1.2815515655446

Then, (12.1 - 12) = (1.2815515655446 - -2.5758293035489)σ, so σ = (12.1 - 12)/(1.2815515655446 - -2.5758293035489) = 0.0259243262186605

Then, (12.1 - µ)/σ = z_.9 , so

(12.1 - µ) = z_.9 σ, or

µ = 12.1 - z_.9 σ, or 12.1 - 1.2815515655446 * 0.0259243262186605 = 12.0667766391488

N(12.067, 0.026)

Note that this is not the standard notation for the normal distribution; the second value is usually the variance, which is σ²