Question

Umbrella Corporation purchases a raw material in 55-gallon drums from a supplier. Records for the supplier indicate that the impurity level in the material per drum has a normal distribution with a mean of 3% and a standard deviation of 0.4%. An impurity level of 4% or more in any shipment requires that Umbrella return the entire drum to the supplier.

What is the probability that Umbrella has to return any given shipment?

Answer 1

The probability that Umbrella returns any shipment is 0.0062.

Explanation:

Let X = the impurity level in the material per drum

Then it is provided that,

`X\sim N(\mu = 0.03,\ \sigma=0.004)`

Also if the impurity level is more than or equal to 4% or 0.04 in any shipment, then Umbrella returns the entire drum to the supplier.

Compute the probability that Umbrella returns any shipment as:

`P(X\geq 0.04)=P((X-\mu)/(\sigma)\geq (0.04-0.03)/(0.004)) \\=P(Z\geq 2.5)\\=1-P(Z<2.5)\\=1-0.99379\\=0.00621\\\approx0.0062`

Use the z-table fro left z-scores to determine the probability.

Thus, the probability that Umbrella returns any shipment is 0.0062.