Question

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 235 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than 0.02, the entire shipment is returned to the vendor. What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.07? (Round your answer to four decimal places.)

Answer 1

To find the approximate probability that a shipment will be returned if the true proportion of defective cartridges is 0.07, we can use the normal approximation to the binomial distribution. Calculate the probability using the z-score formula based on the sample proportion and the true proportion of defects.

Step-by-step explanation:

To find the probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.07, we need to calculate the probability of the sample proportion being more than 0.02. We can use the normal approximation to the binomial distribution to solve this problem.

The sample proportion follows a normal distribution with mean p and standard deviation sqrt((p(1-p))/n), where p is the true proportion of defective cartridges and n is the sample size. In this problem, p = 0.07 and n = 235. Therefore, the probability can be calculated using the z-score formula:

• z = (0.02 - 0.07) / sqrt((0.07 * 0.93) / 235)
• p(returned) = P(Z > z)

Using a standard normal distribution table or a statistical calculator, we can look up the probability of the z-score and find the approximate probability that the shipment will be returned.

Answer 2

To find the approximate probability that a shipment will be returned if the true proportion of defective cartridges is 0.07, we can use the normal approximation to the binomial distribution. Calculate the probability using the z-score formula based on the sample proportion and the true proportion of defects.

Step-by-step explanation:

To find the probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.07, we need to calculate the probability of the sample proportion being more than 0.02. We can use the normal approximation to the binomial distribution to solve this problem.

The sample proportion follows a normal distribution with mean p and standard deviation sqrt((p(1-p))/n), where p is the true proportion of defective cartridges and n is the sample size. In this problem, p = 0.07 and n = 235. Therefore, the probability can be calculated using the z-score formula:

• z = (0.02 - 0.07) / sqrt((0.07 * 0.93) / 235)
• p(returned) = P(Z > z)

Using a standard normal distribution table or a statistical calculator, we can look up the probability of the z-score and find the approximate probability that the shipment will be returned.