Question

In: Statistics and Probability

Businesses often sample products to test the proportion of defectives. Suppose a company that assemble automobiles...

Businesses often sample products to test the proportion of defectives. Suppose a company that assemble automobiles wants to check the quality of batteries it buys from a supplier. Out of each shipment of 1,000 batteries, they will take a sample of 10 and test them. Assuming that, in fact, 2% of the batteries are defective, how likely are they to reject a shipment? Generate the binomial table (Even though it may seem illogical, consider a defective to be a ‘success’ for the purposes of constructing and interpreting your table.) Specify probabilities in informal and notational terms, and show your work:

1) If the company has a policy of rejecting a shipment if they find any defective batteries, how likely are they to accept a given shipment (4 decimal places)?

2) If the company changes policy to accept if no more than one battery is defective, how likely are they to accept a given shipment (4decimal places)?

3) What is the expected value of the number of defective batteries in the sample of 10 ? Imagine the factory has a bad run this month, and their defective rate doubles (to 4%). What will be the chances of the company accepting one of these shipments (assuming they follow the strict policy of rejecting when any defects are found)?

4) Write a single binom.dist formula you can use to calculate this probability:

5) Now suppose the factory is having a terrible, horrible, no good, very bad month, and its defective rate shoots up to 10%.

a) How likely is acceptance of the shipment, assuming acceptance only if no defectives are found?

b) How would you describe the binomial distribution for this scenario?

Expert Solution

The binomial distribution has parameters . The random variable is the number of defective in samples. . The binomial table is constructed using EXCEL as below. The second cell in the second column has formula =BINOMDIST(F8,10,0.02,FALSE)

Look up the above table.

1)The probability of finding any defective items is . The probability of accepatance is .

2)The probability of accepatance is

3) The expecetd value of binomial distribution is .

When , the probability of accepatance is .

4) The formula is

orchestra answered 2 years ago

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