Answer to Question #170642 in Statistics and Probability for EUGINE HAWEZA

Question

 A <b><i>wholesale</i></b> <b><i>distribution</i></b> of a tablet <b><i>compression</i></b> machine finds that the annual demand for the product is normal distribution with mean 140 and standared deviation of 15. ifhe orders only once in a year. What quantity should be ordered to ensure that there is only 5% chance of running short

Answer 1

We suppose that the annual demand be denoted by the random variable X.

$Z = \frac{X-140}{15}$

Since the area between the mean and the given value of X is 0.45 (0.5-0.05), therefore from the table we get this area of 0.45 corresponding to Z = 1.64.

$1.64 = \frac{X-140}{15} \\ 24.6 = X -140 \\ X = 164.6$

We can take the order value 164.6 as 165 by rounding if the ordered value is a whole unit.