Question

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected

Answer 1

Answer:

Given

Sneeze Revisited According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will cover his or her mouth with a tissue, handkerchief, or elbow (the method recommended by public health officials) is 0.047. Suppose you sit on a bench in a mall and observe people’s habits as they sneeze.

a)

Let x be the number of person do not cover their mouth.

Let the probability a randomly selected individual will cover his or her mouth with a tissue, handkerchief, or elbow (the method recommended by public health officials) is 0.047.

P=0.047

Let the sample size n=15

Let x follows binomial distribution with parameter np.

Here n=15 and P=0.047

The probability of a mass function of a binomial distribution is

P(X=x) = , for x = 0, 1, 2, . . . , n

Here we find the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing.

P(X=2) =

P(X=2) = 0.124049

Therefore the probability exactly 2 cover their mouth with a tissue, handkerchief, or elbow is 0.124049 .

b)

Let the probability that among 15 randomly observed individuals fewer than 3 cover their mouth with a tissue, handkerchief, or elbow.

We know that

Here P=0.047

Let the sample size n=15

Let x follows binomial distribution with parameter np.

Here n=15 and P=0.047

The probability of a mass function of a binomial distribution is

P(X=x) = , for x = 0, 1, 2, . . . , n

Here we find the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing.

P(X<3) = ++

P(X<3) = 0.485728+0.359327+0.124049

P(x<3) = 0.969104

C)

Yes.We would be surprised if, after observing 15 randomly observed individuals, more than 4 covered the mouth with a tissue, handkerchief, or elbow.

Here n=15 and P=0.047

The probability of a mass function of a binomial distribution is

P(X=x) = , for x = 0, 1, 2, . . . , n

P(x>4) = +++...+

P(x>4) = 0.000425573+..+1.20633E-20

P(x>4) = 0.000462885

P(x>4) 0.0005.

I am surprised that the probability of more than 4 individuals covered their mouth with a tissue, handkerchief, or elbow out of 15 individuals is approximately 0.05% which is extremely small.

Step-by-step explanation: