Question

13. According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.

(a) What is the probability that among 18 randomly observed individuals exactly 8 do not cover their mouth when sneezing?

(b) What is the probability that among 18 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?

(c) Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? Why?

(a) The probability that exactly 8 individuals do not cover their mouth is

(Round to four decimal places as needed.)

(b) The probability that fewer than 5 individuals do not cover their mouth is

(Round to four decimal places as needed.)

(c) Fewer than half of 18 individuals covering their mouth (1) _______ be surprising because the probability of observing fewer than

half covering their mouth when sneezing is _______ which (2) _______ an unusual event.

(Round to four decimal places as needed.)

(1) Would not would

(2) is not is

Answer 1

13. Here it is given that p=0.267 is same for all, n=18 is constant, events are independent and only two outcomes

As all the properties of binomial distribution is satisfied, we will use binomial distribution to find required probability

a

P(z = 8) = BİŅOM DIST(8. 18.0.267.0) = 0.0506

b.

P(z < 5) = P(z < 4) BINOMDIST(4. 18. 0.267.1) = 0.4521

c.

P(z < 9)-P(z < 8) BINOM DIST(8. 18. 0.267, 1) 0.9706

d. Typically, we say that an event with a probability less than 5% is unusual,

Here it is not less than 0.05, so answer is

Fewer than half of 18 minutes covering their mouth would not be surprising because probability of observing fewer than half covering their mouth wen sneezing is 0.9706, which is not an unusual event

Answer 2

The answer is correct except c)

Instead of 0.267 in formula, use 0.733, which is calculated as (1-0.267).

In this case, answer c) is: p(x<9) = BINOMDIST (8;18;0.733;1) = 0.0089