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Chapter 5: Q6 (page 209)

Identifying Binomial Distributions. In Exercises 5鈥�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 use the YSORT method and give birth to 291 babies, the genders of the babies are recorded.

Short Answer

Expert verified

The given situation can be approximated using the binomial distribution as the gender of a baby has exactly twopossible outcomes, and the rest of the assumptions are also fulfilled.

Step by step solution

01

Given information

Out of 291 couples who used the YSORT method to give birth to 291 babies, the genders of the 291 babies are recorded.

02

Assumptions of binomial distribution

The following assumptions of the binomial distribution should be satisfied:

  • The procedure should have a finite number of trials.
  • Independent trials
  • Each trial should have outcomes that are of exactly two kinds: success and failure.
  • The likelihood of success (denoted as p) remainsthe same for all the trials.
03

Fulfilment of assumptions

The number of trials is fixed and holds a value equal to 291.

All trials are independent as 291 different couples are used to produce 291 babies.

It can be seen that the trial involves recording the gender of the baby. Moreover, the gender of a baby has exactly two possible outcomes.

Since all the 291 couples have used the same YSORT method, the probability of success (boy) will remain the same for all trials.

Since the procedure follows all the above assumptions,the given situation can be modeled using the binomial distribution.

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Most popular questions from this chapter

In Exercises 25鈥�28, find the probabilities and answer the questions.

Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

d. If we randomly select five adults, is 1 a significantly low number who say that they were too young to get tattoos?

Significance with Range Rule of Thumb. In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel鈥檚 famous experiments).

Hybrids Assume that offspring peas are randomly selected in groups of 16.

a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 16.

b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

c. Is a result of 7 peas with green pods a result that is significantly low? Why or why not?

Groups of people aged 15鈥�65 are randomly selected and arranged in groups of six. The random variable xis the number in the group who say that their family and / or partner contribute most to their happiness (based on a Coca-Cola survey). The accompanying table lists

the values of xalong with their corresponding probabilities. Does the table describe a probability distribution? If so, find the mean and standard deviation.

x

P(x)

0

0+

1

0.003

2

0.025

3

0.111

4

0.279

5

0.373

6

0.208

In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

What does the probability of 0+ indicate? Does it indicate that among five randomly selectedflights, it is impossible for none of them to arrive on time?

x

P(x)

0

0+

1

0.006

2

0.051

3

0.205

4

0.409

5

0.328

In Exercises 15鈥�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 6 girls in 8 births.

b. Find the probability of getting 6 or more girls in 8 births.

c. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)?

d. Is 6 a significantly high 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
See all solutions

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