Essentials of Statistics, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780321926739
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 5, Problem 1FDD
FROM DATA TO DECISION
Critical Thinking: Did Mandal’s results from plant hybridization experiments contradict his theory?
Gregor Mendel conducted original experiments to study the genetic train of pea plaits. In 1865 he wrote “Experiments in Plant Hybridization.” which was published in Proceedings of the Natural History Society Mendel presented a theory that when there are two inheritable, 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/yd low 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 offspring 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’s theory. 3/4 of the offspring should have green pods, bat the actual number of plants with green pods was 428. So the proportion of offspring with green pods to the total number of offspring b 428/580 = 0.738. Mendel expected a proportion of 3/4 or 0.75, but his actual mull is a proportion off 0.738.
- a. Assuming that P(green pod) = 3/4, find the
probability that among 580 offspring, the number of peas with green pods b exactly 428. - b. Assuming that P(green pod) = 3/4. find the probability that among 580 offspring, the number of peas with green pods b 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 “Identifying Significant Results with Probabilities” in Section 5-1.)
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Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
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AAB (ANB) U (BA) = (AUB) (AB),
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16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
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Chapter 5 Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
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