Question

1. A laboratory worker finds that 3% of his blood samples test positive for the HIV virus. In a random sample of 70 blood tests, what is the mean number that test positive for the HIV virus? (Round your answer to 1 decimal place)

2. A laboratory worker finds that 3% of his blood samples test positive for the HIV virus. In a random sample of 70 blood tests, what is the standard deviation of the number of people that test positive for the HIV virus? (Round your answer to 1 decimal place)

3.

In a certain college, 33% of the physics majors belong to ethnic minorities. If 8 students are selected at random from the physics majors, what is the probability that more than 5 belong to an ethnic minority?

a. 0.0187

b. 0.9154

c. 0.0846

d. 0.0659

4. Only 35% of the drivers in a particular city wear seat belts. Suppose that 20 drivers are stopped at random what is the probability that exactly four are wearing a seatbelt? (Round your answer to 4 decimal places)

5. Is the binomial distribution appropriate for the following situation:

Joe buys a ticket in his state’s “Pick 3” lottery game every week; X is the number of times in a year that he wins a prize.

a. yes

b. no

c. cannot be determined

Answer 1

1. The mean number that test positive for the HIV virus = 0.03

2. The standard deviation of the number of people that test positive for the HIV virus

3. Let X denotes the number of physics majors who belong to ethnic minorities in a random sample of 8 students.

X ~ Binomial(n = 8, p = 0.33)

The probability mass function of X is

The probability that more than 5 belong to an ethnic minority

4. Let Y denotes the number of drivers who are wearing a seat belt in a random sample of 20 drivers.

Y ~ Binomial(n = 20, p = 0.35)

The probability mass function of Y is

Now,

The probability that exactly four are wearing a seat belt

5. b) no, this is an example of poisson distribution.