Answer:
The probability that Umbrella returns any shipment is 0.0062.
Step-by-step explanation:
Let X = the impurity level in the material per drum
Then it is provided that,
[tex]X\sim N(\mu = 0.03,\ \sigma=0.004)[/tex]
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:
[tex]P(X\geq 0.04)=P(\frac{X-\mu}{\sigma}\geq \frac{0.04-0.03}{0.004}) \\=P(Z\geq 2.5)\\=1-P(Z<2.5)\\=1-0.99379\\=0.00621\\\approx0.0062[/tex]
Use the z-table fro left z-scores to determine the probability.
Thus, the probability that Umbrella returns any shipment is 0.0062.
