Question

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. click the icon to view the table. probability distribution for x x p(x) 0 0.176 1 0.377 2 0.301 3 0.118 4 0.021 5 0.007 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 the result from part (b)? a. since the probability of getting 4 sleepwalkers is the result from part (a), this is the relevant probability. b. since the probability of getting 4 or more sleepwalkers is the probability of the given or more extreme result, the result from part (b) is the relevant probability. c. since the probability of getting 5 sleepwalkers is less likely than getting 4 sleepwalkers, the result from part (a) is the relevant probability. d. since the probability of getting fewer than 4 sleepwalkers is the complement of the result from part (b), this 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. no, since the appropriate probability is greater than 0.05, it is not a significantly high number. b. yes, since the appropriate probability is less than 0.05, it is 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 greater than 0.05, it is a significantly high number.

Explanation:

Part (a)

Step1: Identify P(4) from table

From the probability distribution table, when \( x = 4 \), \( P(4)=0.021 \).

Step1: Define "4 or more"

"4 or more" means \( x = 4 \) or \( x = 5 \).

Step2: Sum P(4) and P(5)

From the table, \( P(4) = 0.021 \) and \( P(5)=0.007 \). So, \( P(4 \text{ or more})=P(4)+P(5)=0.021 + 0.007=0.028 \).

To determine if a number is significantly high, we use the probability of the event or more extreme events (more sleepwalkers in this case). For \( x = 4 \), the more extreme event is \( x = 5 \), so we need \( P(4 \text{ or more}) \), which is part (b)'s result. Option B states this correctly.

Answer:

\( 0.021 \)

Part (b)