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Chapter 5: Q2 (page 195)
Is the random variable given in the accompanying table discreteor continuous? Explain.
Number of Girls x | P(x) |
0 | 0.063 |
1 | 0.25 |
2 | 0.375 |
3 | 0.25 |
4 | 0.063 |
The variable x is a discrete random variable.
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In Exercises 5 and 6, refer to the given values, then identify which of the following is most appropriate:discrete random variable, continuous random variable, ornot a random variable.
a. Grades (A, B, C, D, F) earned in statistics classes
b. Heights of students in statistics classes
c. Numbers of students in statistics classes
d. Eye colors of statistics students
e. Numbers of times statistics students must toss a coin before getting heads
Are the values found in Exercise 2 statistics or parameters? Why?
Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.
News Source Based on data from a Harris Interactive survey, 40% of adults say that they prefer to get their news online. Four adults are randomly selected.
a. Use the multiplication rule to find the probability that the first three prefer to get their news online and the fourth prefers a different source. That is, find P(OOOD), where O denotes a preference for online news and D denotes a preference for a news source different from online.
b. Beginning with OOOD, make a complete list of the different possible arrangements of those four letters, then find the probability for each entry in the list.
c. Based on the preceding results, what is the probability of getting exactly three adults who prefer to get their news online and one adult who prefers a different news source.
Critical Thinking: Did Mendel鈥檚 results from plant hybridization experiments contradict his theory? Gregor Mendel conducted original experiments to study the genetic traits of pea plants. In 1865 he wrote 鈥淓xperiments in Plant Hybridization,鈥� which was published in Proceedings of the Natural History Society. Mendel presented a theory that when there are two inheritable traits, one of them will be dominant and the other will be recessive. Each parent contributes one gene to an offspring and, depending on the combination of genes, that offspring could inherit the dominant trait or the recessive trait. Mendel conducted an experiment using pea plants. The pods of pea plants can be green or yellow. When one pea carrying a dominant green gene and a recessive yellow gene is crossed with another pea carrying the same green>yellow genes, the offspring can inherit any one of these four combinations of genes: (1) green/green; (2) green/yellow; (3) yellow/green; (4) yellow/yellow. Because green is dominant and yellow is recessive, the offspring pod will be green if either of the two inherited genes is green. The offspring can have a yellow pod only if it inherits the yellow gene from each of the two parents. Given these conditions, we expect that 3/4 of the o搂spring peas should have green pods; that is, P(green pod) = 3/4. When Mendel conducted his famous hybridization experiments using parent pea plants with the green/yellow combination of genes, he obtained 580 offspring. According to Mendel鈥檚 theory, 3/4 of the offspring should have green pods, but the actual number of plants with green pods was 428. So the proportion of offspring with green pods to the total number of offspring is 428/580 = 0.738. Mendel expected a proportion of 3/4 or 0.75, but his actual result is a proportion of 0.738.
a. Assuming that P(green pod) = 3/4, find the probability that among 580 offspring, the number of peas with green pods is exactly 428.
b. Assuming that P(green pod) = 3/4, find the probability that among 580 offspring, the number of peas with green pods is 428 or fewer.
c. Which of the two preceding probabilities should be used for determining whether 428 is a significantly low number of peas with green pods?
d. Use probabilities to determine whether 428 peas with green pods is a significantly low number. (Hint: See 鈥淚dentifying Significant Results with Probabilities鈥� in Section 5-1.)
For the accompanying table, is the sum of the values of P(x)
equal to 1, as required for a probability distribution? Does the table describe a probability distribution?
Number of Girls x | P(x) |
0 | 0.063 |
1 | 0.250 |
2 | 0.375 |
3 | 0.250 |
4 | 0.063 |
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