Download Mixed Binomial, Geometric and Random Variable

AP Statistics
Mixed Binomial, Geometric and Random Variable Practice
1. According to a recent Census Bureau report, 12.7% of Americans live below the poverty level.
Suppose you plan to sample at random 100 Americans and count the number of people who live
below the poverty level.
a. What is the probability that you count exactly 10 in poverty?
b. What is the probability that you start taking the random sample and you find the first person in
poverty on the 8th person selected?
c. How many people would you expect to be in poverty?
2. Dr. Fidgit developed a test to measure boredom tolerance. He administered it to a group of 20,000
adults between the ages of 25 and 35. The possible scores were 0, 1, 2, 3, 4, 5, and 6, with 6
indicating the highest tolerance to boredom. The following is the probability distribution:
X
0
1
2
3
4
5
6
P( X ) 0.07 013
.
018
.
0.30 0.22 0.08 0.02
a. Find P( X  4)
b. Find P(1  X  4)
c. Find P( X  2)
d. If 30 adults were randomly selected, what is the probability that 10 had a boredom score less
than or equal to 2?
e. If 10 adults were randomly selected, what is the probability that only one or two adults would
have the lowest boredom score?
f. What is the probability that the first adult that scored at least a 4 was the 5th adult chosen?
3. A potential buyer will sample videotapes from a large lot of new videotapes. If she finds at least one
defective one, she’ll reject the entire lot. If ten percent of the lot is defective, what is the probability
that she’ll find a defective tape by the 4th videotape?
4. A game is played with a spinner on a circle, like the minute hand on a clock. The circle is marked
evenly from 1 to 100. The player spins the spinner and the resulting number is the number of seconds
the player is given to solve a randomly selected mathematics problem. Suppose there are 30 students
playing in the class.
a. What is the probability that 10 of the students received over a minute to solve the problem?
b. What is the probability that exactly half of the students received 30 or less seconds?
c. What is the probability that the fourth student was the first to receive a minute or less?
d. What is the probability that half of the students received 45 seconds or more?
e. What is the probability that a minute or more was received by the 10th student?
5. A certain golfer makes her putts 60% of the time.
a. If she putts 10 times, what is the probability that she will make half or less?
b. What is the probability that the 3rd putt was the first one she made?
c. If she putts 8 times, what is the probability that she will make 5 or more putts?
d. What is the probability that the 4th putt was the first one she misses?
6. Michael Jordan, Allen Iverson, and Vince Carter will have their picture put in the new boxes of
Wheaties.
a. Create a distribution of the chances of landing a MJ poster up to the 5th box.
b. How will the distribution appear different if the Allen Iverson poster is discontinued?
c. How will the distribution appear different if Kobe Bryant, Shaquille O’Neal and Tim Duncan
are added?
7. Brandon and Kathy are competing to sell the most boxes of holiday cards for their high school band's
fundraiser. The following probability density functions display their daily possibilities.
B
0 1 2 3
K
0 1 2
P(B) .1 .5 .2 .2
P( K ) .1 .2 .7
a. What is the expected value, variance and standard deviation for the number of boxes of
holiday cards sold by Brandon.
b. What is the expected value, variance and standard deviation for the number of boxes of
holiday cards sold by Kathy.
c. How many total cards per day would you expect them to sell? Standard deviation?
d. Who would you expect to sell more cards per day? How many more? Standard deviation?
e. If the profit from each box of holiday cards is $3.50, how much total money would they bring
in per day? Standard deviation?
8. Suppose X and Y are random variables with  X =10,  X =2,  Y =7,  Y =3. Given that X and Y are
independent variables, calculate the following:
2
 2X

 Y28 
2 X 
Y 8 =
10 X 
4 X 1 
 X Y =
 10 X 
 42X 1 
 X2 Y =
10Y 
 X Y =
 X2 =
 10Y 
 X2 Y =
 X Y =
9. Many manufacturers have quality control programs that include inspection of incoming materials for
defects. Suppose that a computer manufacturer receives computer boards in lots of five. Two boards
are selected from each lot for inspection. Each possible outcome is a pair of numbers.
a. List the ten possible outcomes.
b. Suppose boards 1 and 2 are the only defective boards in a lot of five. Define X as the number
of defective boards observed among those inspected. Find the probability distribution.