Question

5.1 12

The accompanying table describes the random variable x, the numbers of adults in groups of five who reported sleepwalking. Complete parts (a) through (d) below.

x P(x)

0 0.169

1 0.361

2 0.319

3 0.119

4 0.027

5 0.005

**A.**

Find the probability of getting exactly 4 sleepwalkers among 5 adults.

(Type an integer or a decimal. Do not round.)

**B.** Find the probability of getting 4 or more
sleepwalkers among 5 adults.

(Type an integer or a decimal. Do not round.)

**c.** Which probability is relevant for
determining whether 4 is a significantly high number of
sleepwalkers among 5 adults: the result from part (a) or part
(b)?

A.

Since the probability of getting fewer than 4 sleepwalkers is the complement of the result from part (b), this is the relevant probability.

B.

Since the probability of getting 5 sleepwalkers includes getting 4 sleepwalkers, the result from part (b) is the relevant probability.

This is the correct answer.

C.

Since the probability of getting 4 sleepwalkers is the result from part (a), this is the relevant probability.

D.

Since the probability of getting 5 sleepwalkers is less likely than getting 4 sleepwalkers, the result from part (a) is the relevant probability.

**d.** Is 4 a significantly high number of 4
sleepwalkers among 5 adults? Why or why not? Use 0.05 as the
threshold for a significant event.

A.

Yes, since the appropriate probability is greater than 0.05, it is a significantly high number.

B.

No, since the appropriate probability is greater than 0.05, it is not a significantly high number.

C.

No, since the appropriate probability is less than 0.05, it is not a significantly high number.

D.

Yes, since the appropriate probability is less than 0.05, it is a significantly high number.

Answer #1

A) P(X = 4) = 0.027

Therefore, the probability of getting exactly 4 sleepwalkers
among 5 adults is **0.027**

B) P(X >= 4) = P(X = 4) + P(X = 5) = 0.027 + 0.005 = 0.032

Therefore, the probability of getting 4 or more sleepwalkers
among 5 adults is **0.032**

C) Since the probability of getting 4 sleepwalkers is the result from part (a), this is the relevant probability.

D) Yes, since the appropriate probability is less than 0.05, it is a significantly high number.

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