Please help ... its about normal distribution!! funny question

[student in need]

I'm doing some revision and i came across this question and i can't work out how to start it.

In a food manufacturing plant, the weight of cereal is normally distributed with a mean of 200.6 gms and a standrad deviation of 1.8Gms.

Assuming the same standard deviation, how large would the mean weight have to be in order for less than 1% of packets to be rejected as underfilled.

packets are rejects if they are under 198 gms.


HELP this is driving me mental!

[Rassis]

Hi,

If you consider Z (the standard normal distribution) = (x - average) / standard deviation, and knowing that Z(0,01) from Normal tables or from EXCEL doing NORMSINV(0,01), you get Z = -2,32635. Then you solve x from the equation: -2,32635 = (198 - new average) / 1,8 and you get the new average = 202,1874.

You can confirm this result coming back to EXCEL and computing NORMDIST(198; 202,1874; 1,8; 1) and you will get 0,01 again.

Be happy.