Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 59 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 5​% rate of​ defects, what is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

Please show how to find the answer in a calculator, NOT in a written equation

Answer 1

Solution

A pharmaceutical company receives large shipments of aspirin tablets.

P(x 1) = p(0 x1) = p (x= 0,1)

p (x=0) + (x=1)

p(x=0) = (0.05)⁰(1-0.05)¹⁰ = 1(0.05)⁰ (0.98)¹⁰=9.5703125

P(x=1)= (0.05)¹(1-0.02)¹(1-0.02)⁹ = 10 (0.05)¹(0.09)⁹=1.937102445

p (x=0) + (x=1)

9.5703102445-1.937402445 =7.63290

P(x 1)= 7.63290

there is sufficient evidence to support the claim that it costs more than average to produce an action movie

Answer 2

To find the probability that the whole shipment will be accepted, we need to calculate the probability that there is at most one defective tablet in the sample of 59 tablets. We can use a binomial distribution to solve this problem.

In this case, the probability of a defective tablet is 0.05, and the sample size is 59. We want to find the probability of having 0 or 1 defective tablets. Using a calculator, we can perform the following steps:

1. Open a binomial probability calculator or use a scientific calculator with a binomial probability function.

2. Enter the parameters:

• Number of trials (n): 59

• Probability of success (p): 0.05

• Number of successes (x): 0 or 1 (we want the probability of having 0 or 1 defective tablets)

Calculating the probability for x = 0:

• For x = 0, enter the values into the calculator and calculate the binomial probability.

• The result will give you the probability of having exactly 0 defective tablets in the sample.

Calculating the probability for x = 1:

• For x = 1, enter the values into the calculator and calculate the binomial probability.

• The result will give you the probability of having exactly 1 defective tablet in the sample.

Finally, add the probabilities obtained for x = 0 and x = 1 to find the overall probability of accepting the whole shipment.

The probability of accepting the whole shipment is the sum of the probabilities obtained for x = 0 and x = 1.

Using a calculator, you can find the probability of accepting the whole shipment based on the above steps.