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.
a. find the probability of getting exactly 4 sleepwalkers among 5 adults.
0.021 (type an integer or a decimal. do not round.)
b. find the probability of getting 4 or more sleepwalkers among 5 adults.
0.025 (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
a. 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
b. since the probability of getting fewer than 4 sleepwalkers is the complement of the result from part (b), this 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 4 sleepwalkers is the result from part (a), 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. yes, since the appropriate probability is less than 0.05, it is a significantly high number
b. yes, since the appropriate probability is greater 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. no, since the appropriate probability is greater than 0.05, it is not a significantly high number.

Explanation:

Step1: Identify probability for part (a)

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

Step2: Calculate probability for part (b)

To get 4 or more sleep - walkers among 5 adults, we add \(P(4)\) and \(P(5)\). So \(P(X\geq4)=P(4)+P(5)=0.021 + 0.004=0.025\)

Step3: Determine relevant probability for part (c)

To determine if 4 is a significantly high number, we consider the probability of getting 4 or more (the given or more extreme result). So the relevant probability is from part (b).

Step4: Determine significance for part (d)

The probability of getting 4 or more sleep - walkers is \(P(X\geq4) = 0.025\). Since \(0.025<0.05\), 4 is a significantly high number.

Answer:

a. \(0.021\)
b. \(0.025\)
c. A. 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.
d. A. Yes, since the appropriate probability is less than 0.05, it is a significantly high number.