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In Exercises 21鈥25, refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from 鈥淧revalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General Population,鈥 by Ohayon et al., Neurology, Vol. 78, No. 20).

Using Probabilities for Identifying Significant Events

a.Find the probability of getting exactly 1 sleepwalker among 5 adults.

b. Find the probability of getting 1 or fewer sleepwalkers among 5 adults.

c. Which probability is relevant for determining whether 1 is a significantly lownumber of sleepwalkers among 5 adults: the result from part (a) or part (b)?

d. Is 1 a significantly low number of sleepwalkers among 5 adults? Why or why not?

x

P(x)

0

0.172

1

0.363

2

0.306

3

0.129

4

0.027

5

0.002

Short Answer

Expert verified

a. The probability of getting exactly 1 sleepwalker among 5 adults is 0.363.

b. The probability of getting 1or fewer sleepwalkers among 5 adults is 0.535.

c. The probability computed in part (b) is relevant for concluding whether 1 sleepwalkers is significantly low or not.

d. No, 1 is not a significantly low number of sleepwalkers among 5 adults.

Step by step solution

01

Given information

The probability distribution for the number of adults in groups who reported sleepwalking is provided.

02

Calculate the probability of getting exactly 4 sleepwalkers among 5 adults

a.

Letx be the number of sleepwalkers in a group of five.

Using the probability distribution table, the probability corresponding to 1 sleepwalker among 5 adults is 0.363.

Thus, the probability of getting exactly 1 sleepwalker among 5 adults is 0.363.

03

Calculate the probability of getting 1or fewer sleepwalkers among 5 adults

b.

Using the probability distribution table, the probability corresponding to 1 sleepwalker is 0.363.

The probability corresponding 0 sleepwalkers is 0.172.

The probability of getting 1 or fewer sleepwalkers among 5 adults is computed as:

Px1=Px=0+Px=1=0.172+0.363=0.535

Thus, the probability of getting 1 or fewer sleepwalkers among 5 adults is 0.535.

04

State which probability is relevant to determine whether 1 is a significantly low number of sleepwalkers among 5 adults

c.

The following probability expression is used to determine if the given sample value is significantly low or not:

Pxorfewer0.05

If the above expression holds true, then the number of successes for that event can be considered significantly low.

Here, part (b) computes the probability of 1 or fewer sleepwalkers in a sample of 5 adults.

Therefore, the probability computed in part (b) is relevant for concluding whether 1 sleepwalker is significantly low or not.

05

Check whether 1 is a significantly low number of sleepwalkers among 5 adults

d.

Since the probability of 1 or fewer number of sleepwalkers in a sample of 5 adults is 0.535, which is not less than or equal to 0.05, thus, the number of sleepwalkers equal to 1 cannot be considered significantly low.

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