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Chapter 5: Q 3 (page 220)
Are the values found in Exercise 2 statistics or parameters? Why?
The values are parameters.
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In Exercises 9–16, use the Poisson distribution to find the indicated probabilities.
Murders In a recent year, there were 333 murders in New York City. Find the mean number of murders per day, then use that result to find the probability that in a day, there are no murders. Does it appear that there are expected to be many days with no murders?
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 15–20, assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n = eight 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 no more than 2.
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.
Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, was designed to increase the likelihood that a baby will be a boy. When 291 couples used the YSORT method and gave birth to 291 babies, the weights of the babies were recorded.
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.
AAA Batteries AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic. When purchasing bulk orders of AAA batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 2000 AAA batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
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