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In: Statistics and Probability

A certain large shipment comes with a guarantee that it contains no more than 25% defective...

A certain large shipment comes with a guarantee that it contains no more than 25% defective items. If the proportion of items in the shipment is greater than 25%, the shipment may be returned. You draw a random sample of 12 items and test each one to determine whether it is defective.

a. If in fact 25% of the items in the shipment are defective (so that the shipment is good, but just barely) what is the probability that 7 or more of the 12 sampled items are defective?

b. Based on the answer to part (a), if 25% of the items in the shipment are defective would 7 defectives in a sample of size 12 be an unusually large number?

c. If you found that 7 of the 12 sample items were defective, would this be convincing evidence that the shipment should be returned?

d. If in fact 25% of the items in the shipment are defective, what is the probability that 2 or more of the 12 sampled items are defective?

e. Based on the answer to part (d), if 25% of the items in the shipment are defective, would 2 defectives in a sample of 12 be an unusually large number?

f. If you found that 2 of 12 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.

g. Find the mean,

h. Find the variance,

i. Find the standard deviation,

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Expert Solution

orchestra answered 2 years ago
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