Question

A fashion retailer buys a line of blouse of $10 each from its supplier. The retailer forecasts that its demand is normally distributed with mean of 2100 and a standard deviation of 1200 unit. Each blouse is sold at $22. Unsold blouse would be donated to charity. What is the probability that the retailer sells less than half of its forecast of 2100 units?

Answer 1

Mean , u = 2100

Std deviation ,s = 1200

Half of forecast, X = 2100/2 = 1050

Z-score = (X -u ) / s = (1050-2100) / 1200 = -0.875

In excel, use normsdist( -0.875) to get probability = 0.1908 or 19.08% (This is exact value from excel)

If you see standard normal distribution table, Z = -0.87 , p =0.1921 , for Z = -0.88 , p = 0.1894. Hence, p = 0.1908 (somewhere in between two values)

probability that the retailer sells less than half of its forecast of 2100 units = 19.08%