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Chapter 5: Q5 (page 220)
Using the same SAT questions described in Exercise 2, is 8 a significantly low number of correct answers for someone making random guesses?
8 is a significantly low number of correct answers.
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In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n = 8 trials, each with probability of success (correct) given by p = 0.20. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is at least 4.
Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.
LOL In a U.S. Cellular survey of 500 smartphone users, subjects are asked if they find abbreviations (such as LOL or BFF) annoying, and each response was recorded as “yes” or “other.”
Acceptance Sampling. Exercises 35 and 36 involve the method of acceptance sampling, whereby a shipment of a large number of items is accepted based on test results from a sample of the items.
Aspirin The MedAssist Pharmaceutical Company receives large shipments of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 40 tablets, then accept the whole batch if there is only one or none that doesn’t meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
In Exercises 15–20, refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.
Using Probabilities for Significant Events
a. Find the probability of getting exactly 1 girl in 8 births.
b. Find the probability of getting 1 or fewer girls in 8 births.
c. Which probability is relevant for determining whether 1 is a significantly low number ofgirls in 8 births: the result from part (a) or part (b)?
d. Is 1 a significantly low number of girls in 8 births? Why or why not?
Number of girls x | P(x) |
0 | 0.004 |
1 | 0.031 |
2 | 0.109 |
3 | 0.219 |
4 | 0.273 |
5 | 0.219 |
6 | 0.109 |
7 | 0.031 |
8 | 0.004 |
In Exercises 1–5, assume that 74% of randomly selected adults have a credit card (based on results from an AARP Bulletin survey). Assume that a group of five adults is randomly selected.
If all five of the adults have credit cards, is five significantly high? Why or
why not?
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