Need the Standard Deviation and Mean... please help ASAP!!!?

Question

There is an expected demand of 20,000 units, with a .90 probability that the demand would be between 10,000 units and 30,000 units. This is based on a bell curve. What is the mean and standard deviation?

Answer 1

If 90% are between 10,000 and 30,000, then 95% will be less than 30,000 (that is, 5% >30000 and 5% < 10000)

Let S = standard deviation, Z = normal N(0,1) distribution, and X your hypothetical distribution.

Then, P(X < 30000) = P(Z < (30000-20000)/S) = 95%
P(Z < 10000/S) = 95%
From N(0,1) table, P(Z < 1.645) = 95%, so
10000/S = 1.645
S = 6079

Answer 2

You're given the mean -- 20000 units. There is a .9 probability that the demand will be between 10000 units and 30000 units, which means a .1 probability that it will not. Assuming demand is normally distributed, this means that the probability that the demand will be less than 10000 units is .05. Consulting your normal table, .05 probability occurs at a z-score of -1.645, so -10000 units is -1.645σ, so simple division reveals σ ≈ 6079 units.