# Calculating binomial probabilities

Two-liter plastic bottles used for bottling cola are shipped in lots of 100. Suppose the lots are 5 percent defective. Some bottles leak, some are too small, and so forth.

a. In the sample of 100, how many of the bottles would you expect to be defective? What

is the standard deviation?

b. Tell why this situation meets the binomial assumptions.

c. What is the probability that a shipment of plastic bottles contains 8 or more defectives?

d. What is the probability that between 8 and 10 bottles are defective?

e. What is the probability that there are exactly 8 defectives?

f. What is the probability of no defectives?

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#### Solution Summary

This solution shows how to calculate probabilities related to a binomial distribution and shows how to find the mean, variance and standard deviation of a binomial distribution.