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:
