[QUOTE=Captain SoamesIn order to solve this question I used Z = Mean - LSL / Sigma

[/quote]

So far it's OK.

That doesn't seem right. You want z s.th. Prob(Z > z) = 0.5% = 0.005. That leads to z = 2.57. Use this value of z in your calculationZ = .05 or .69146

... and you'll get the correct LSL.M = 5000

Sigma = 50

.69146 = 5000 - LSL / 50

LSL = 5000 - ( 50 x .69146 )

LSL = 4965.43

.0228 is the probability of being more than 2 standard deviations below the mean. So the mean minus 2 std dev equals 32. From that you can find the mean .The next question I believe uses Z = USL - Mean / Sigma

If x is normally distributed with mean u and standard deviation four,

and given the probability that x is less, than 32 is 0.0228, find the

value of u