Question

1. Suppose it has been estimated that 60% of American victims of health care fraud are senior citizens and that 10 victims are randomly selected.

a) What is the probability that exactly 4 of the victims are senior citizens?

b) What is the probability that at least 8 of the victims are senior citizens?

c) Determine the expected value.

d) Determine the standard deviation.

2. Suppose that 9% of all men cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals. Suppose that 8 men are randomly selected.

a) What is the probability that exactly 2 of the men will have this type of color blindness?

b) What is the probability that at least one of the men will have this type of color blindness?

c) Determine the expected value.

d) Determine the standard deviation.

3. Suppose it has been estimated that 68% of all Albanian Airlines flights are on time, and that 12 flights are randomly selected.

a) What is the probability that fewer than three of the flights were on time.

b) What is the probability that more than ten of the flights were on time.

c) Determine the expected value.

d) Determine the standard deviation.

Answer 1

1.

given that 60% of American victims of health care fraud are senior citizens so

P(victims of health care fraud are senior citizens)=p=0.6

here n=10

let X is the number of victims out of 10 that are senior citizens so X~Bin(10,0.6)

so

a)

we have to find P(X=4)

now

b)

we have to find P(X>8)

now

c)

expected value =E(X)=n*p=10*0.6=6

d)

2.

Probability of man color blindness =p=0.09

n=8

let X is number of color blind peoples out of 8 so

X~Bin (8,0.09)

a)

we have to find P(X=2)

b)

P(X>1)=?

c)

E(X) =n*p=8*0.09 =0.72

d)

3.

P(Albanian Airlines flights are on time)=p=0.68

n=12

let X is the number of flights on time out of 12 flights

so X~Bin(12,0.68)

Hence

a)

we have to find P(X<3)

now

b)

we have to find P(X>10)

now

c)

E(X)=n*p=12*0.68=8.16

d)