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.