Intro to Statistics probelm

Wizzliewinks

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When a manufacturing process is working properly only 1 in 80 items manufactured is defective. In order to ensure quality of production, a random sample of items is periodically taken and tested to determine how many items are defective in the sample.

If the company finds random samples of 75 items and calculates the percent defective in the sample:

1) completely describe the sampling distribution of p hat (center,shape,spread)

2) if possible find the probability that more than 2 items in a sample of 75 items is defective. If not possible, explain.
 
When a manufacturing process is working properly only 1 in 80 items manufactured is defective. In order to ensure quality of production, a random sample of items is periodically taken and tested to determine how many items are defective in the sample.

If the company finds random samples of 75 items and calculates the percent defective in the sample:

1) completely describe the sampling distribution of p hat (center,shape,spread)

2) if possible find the probability that more than 2 items in a sample of 75 items is defective. If not possible, explain.
Really need like to see your work - no idea where you are getting stuck, nor what tools you have - nor for that matter which distribution has the name \(\displaystyle \hat{p}\).

What do you know about the population distribution?
How do you apply the sampling theorem?
Do you know the formula for the binary distribution?
Under what circumstances could you not answer (2)?
 
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