estimate the probability

Question

Demand for a product is normally distributed with mean demand equal to 200 units.  There is a 0.95 probability that demand for this produce is between 180 to 220 unites.  Estimate the probability that demand for this product will exceed 195 units?

Answer 1

Since demand is normally distributed with mean μ=200, and P(180<X<220)=0.95, the interval 180 to 220 is symmetric about the mean. For a normal distribution, approximately 95% of observations lie within 1.96 standard deviations of the mean.

Thus, 20 ≈ 1.96σ, so σ ≈ 10.20. We want P(X>195).

Standardizing 195, z=(195−200)/(10.20) ≈ −0.49.

Therefore, P(X>195) = P(Z>−0.49) = P(Z<0.49).

From the standard normal table, P(Z<0.49) ≈ 0.688. So the estimated probability that demand exceeds 195 units is 0.69 or approximately 69%.