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 16 randomly observed individuals exactly 8 do not cover their mouth when sneezing?
(b) What is the probability that among 16 randomly observed individuals fewer than 4 do not cover their mouth when sneezing?
(c) Would you be surprised if, after observing 16 individuals, fewer than half covered their mouth when sneezing? Why?

a.  P(X=8)=0.0277

b.  P(X<4)=0.3460

c. No. P(X<8)=0.9605

Step-by-step explanation:

a. Let x denote the event.

This is a binomial probability distribution problem expressed as

Where

Given that n=16, p=0.267, the probability of exactly 8 people not covering their mouths is calculated as:

Hence, the probability of exactly 8 people not covering their mouths is 0.0277

b. The probability of fewer than 4 people covering their mouths is calculated as:

-We calculate and sum the probabilities of exactly 0 to exactly 3:

Hence, the probability of x<4 is 0.3460

c. Would you be surprised if fewer than half covered their mouths:

The probability  of fewer than half covering their mouths is calculated as:

No. The probability of fewer than half is 0.9605 or 96.05%. This a particularly high probability that erases any chance of doubt or surprise.

the correct answer is x/3+10≥32

hope this !

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.