A certain large shipment comes with a guarantee that it contains no more than 20% defective items. If the proportion of defective items in the shipment is greater than 20%, the shipment may be returned. You draw a random sample of 10 items. Let ? be the number of defective items in the sample. a. If the fact 20% of the items in the shipment are defective (so that the shipment is good, but just barely), what is ?(? ≥ 7)? b. Based on the answer to part (a), if 20% of the items in the shipment are defective, would 7 defectives in a sample of size 10 be an unusually large number? c. If you found that 7 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A certain large shipment comes with a guarantee that it contains no more than 20%
defective items. If the proportion of defective items in the shipment is greater than 20%, the
shipment may be returned. You draw a random sample of 10 items. Let ? be the number of
defective items in the sample.
a. If the fact 20% of the items in the shipment are defective (so that the shipment is good, but
just barely), what is ?(? ≥ 7)?
b. Based on the answer to part (a), if 20% of the items in the shipment are defective, would
7 defectives in a sample of size 10 be an unusually large number?
c. If you found that 7 of the 10 sample items were defective, would this be convincing
evidence that the shipment should be returned? Explain.
d. If in fact 20% of the items in the shipment are defective, what is ?(? ≥ 2)?
e. Based on the answer to part (d), if 20% of the items in the shipment are defective, would
2 defectives in a sample of size 10 be an unusually large number?
f. If you found that 2 of the sample items were defective, would this be convincing that the
shipment should be returned? Explain
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