Binomial Mean & Expectation & Geometric
Name____________________
Part I. Find the mean, variance and standard deviation for the following.
1. A study found that 1% of Social Security recipients are too young to vote. If 800 Social Security
recipients are selected, find the mean, variance, and standard deviation of the number of recipients
who are too young to vote.
2. Find the mean, variance, and standard deviation for the number of heads when 10 coins are tossed.
3. If 2% of automobile carburetors are defective, find the mean, variance, and standard deviation of a
lot of 500 carburetors.
4. It has been reported that 83% of federal government employees use email. If a sample of 200
federal government employees is selected, find the mean, variance, and standard deviation of the
number who use email.
5. A survey found that 21% of Americans watch fireworks on television on July 4. Find the mean,
variance, and standard deviation of the number of individuals who watch fireworks on television if a
random sample of 1000 Americans is selected.
Part II. Find the expectation for the following.
6. A box contains ten $1 bills, five $5 bills and one $20 bill. A person is charged $10 to select one bill.
Find the expectation. Is this a fair game? If not, what do you need to charge to make it fair?
7. A cash prize of $2500 is to be awarded by the PTA. If 1500 tickets are sold at $5 each, find the
expected value of the gain.
8. If a person rolls doubles when he tosses two dice, he wins $50. I charge each person $5 to play.
Would you want to play? Explain. What should I charge to make it fair?
9. If a player rolls two dice and gets a sum of 12, he/she wins $20. If they get a sum of four they win
$10. The cost to play the game is $2. Find the expectation of the game.
10. If a player draws a card (from a normal deck) and gets a red Ace, he/she wins $100. If they get a
face card he/she wins $20. If it costs $10 to play, what is the expectation of the game?
Part III. Solve the following geometric problems using the graphing calculator.
11. A basketball player has made 80% of his foul shots during the season. Assuming the shots are independent, find
the probability that in tonight’s game he
a. misses for the first time on his fifth attempt.
b. makes his first basket on his fourth shot.
c. makes his first basket on one of his first 3 shots.
d. what’s the expected number of shots until he misses?
12. Only 4 % of people have Type AB blood.
a. on average, how many donors must be checked to find someone with Type AB blood?
b. What’s the probability that there is a type AB donor among the first 5 people?
c. What’s the probability that we won’t find a Type AB donor before the tenth person?
13. About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment, and begins
checking potential subjects. What’s the probability that the first colorblind man found will be the sixth person
checked?
14. Based on past experience, Julio believes he has a 60% chance of success when he calls a woman and asks for a
date.
a. What’s the probability that the first success he has is the 4th one asked?
b. What’s the probability that he has success before the 3rd woman called?
c. What’s the probability that Julio is not successful until after the 3 rd woman?
Part IV. Solve the following binomial problems using the calculator.
15. One out of four Americans over 55 has eaten pizza for breakfast. If a sample of 10 Americans over 55 is
selected at random, find the probability that at most three have eaten pizza for breakfast?
16. If 36% of all students owe money before graduating, find the probability that if 200 students are selected, at
least 70 owe money.
17. If 75% of nursing students are able to pass a drug calculation test, find the probability that in a sample of 80,
a. exactly 64 pass the tests
b. more than 60 pass the test
c. at least 50 pass the test
d. at most 58 pass the test
e. less than 62 pass the test