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Chapter 5: Q4 (page 195)

For 100 births, P(exactly 56 girls) = 0.0390 and P(56 or more girls) = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?

Short Answer

Expert verified

56 is not a significantly high number of girls, which is determined by the probability of 56 or more girls in 100 births, which is 0.136.

Step by step solution

01

Given information

The number of births is 100.

The probabilities are given as

PExactly56girls=0.0390P56ormoregirls=0.136

02

 Significantly high probabilities

The probability of an event is significantly high if the possibility of that event or more number of such events is 0.05 or lesser.

Similarly, if the probability of an event or fewer than those is 0.05 or lesser, the event is recognized as significantly low.

03

Check for the count of 56 girls in 100 births

The probability of 56 or more girls in 100 is 0.136, which is greater than 0.05.

This implies that it is likely to obtain 56 or more girls among 100 births.

Therefore, 56 girls are not a significantly high number of girls.

Also, the probability that is relevant to answer the provided question is the probability of 56 or more girls, which is 0.136.

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Most popular questions from this chapter

In Exercises 6–10, 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.

Based on the table, the standard deviation is 0.9 flight. What is the variance? Include appropriate units.

x

P(x)

0

0+

1

0.006

2

0.051

3

0.205

4

0.409

5

0.328

Notation In analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 \(k{m^2}\) . A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying Formula 5-9, identify the values of \(\mu \), x, and e. Also, briefly describe what each of those symbols represents.

Hypergeometric Distribution If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution. If a population has A objects of one type (such as lottery numbers you selected), while the remaining B objects are of the other type (such as lottery numbers you didn’t select), and if n objects are sampled without replacement (such as six drawn lottery numbers), then the probability of getting x objects of type A and n - x objects of type B is

\(P\left( x \right) = \frac{{A!}}{{\left( {A - x} \right)!x!}} \times \frac{{B!}}{{\left( {B - n + x} \right)!\left( {n - x} \right)!}} \div \frac{{\left( {A + B} \right)!}}{{\left( {A + B - n} \right)!n!}}\)

In New Jersey’s Pick 6 lottery game, a bettor selects six numbers from 1 to 49 (without repetition), and a winning six-number combination is later randomly selected. Find the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use A = 6, B = 43, n = 6, and x = 2.)

In Exercises 6–10, 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.

Find the mean of the number of flights among five that 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 21–25, refer to the accompanyingtable, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from “Prevalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General Population,” by Ohayon et al., Neurology, Vol. 78, No. 20).

Use the range rule of thumb to determine whether 4 is a significantly high number of sleepwalkersin a group of 5 adults.

x

P(x)

0

0.172

1

0.363

2

0.306

3

0.129

4

0.027

5

0.002
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