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Algebra 2 – Test #12
Suppose a number is chosen at random from the sample space {5, 7, 9, 11, 13, 15, 17}. Find each probability.
1. P(less than 13)
2. P(odd)
3. P(prime or multiple of 5)
Calculate the following.
4. 5P3
5. 7C4
6. 6!
Indicate whether each situation involves a combination or a permutation. Then solve.
7. You must complete the following six chores: take out the trash, wash the dishes, vacuum the carpet, clean your
room, make your bed, feed the fish. In how many different ways can you do the chores?
Perm/Combo__________
Answer__________
8. Groups of five students must be formed to work on a project. In how many different ways can a group of five be
chosen from a class of 12 students?
Perm/Combo__________
Answer__________
Use Binomial Theorem or Pascal’s Triangle to expand each binomial.
9.
( x  y) 3
10. ( 2r  q ) 4
11. The probability of Joseph making a free throw is 0.6. Binomial Experiment.
Find the probability that he will make exactly four out of the seven free throws in one game.
A spinner is spun. State whether the events are mutually exclusive. Then find P(A or B).
(if they can happen at the same time, they are NOT exclusive events. A king or 7 are exclusive)
12. A = an odd number
B = a multiple of 2
13.
6
A = a number < 3
B = a multiple of 3
1
Mutually Exclusive? ______
Mutually Exclusive? ________
5
2
Probability ________
Probability _________
4
3
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14.
At a store, you buy 8 plums, 4 bananas, 6 apples, and 12 carrots.
a) Find the probability for each item.
plums __________
bananas __________
apples __________
carrots __________
b) Find the probability that one food item chosen at random is a piece of fruit. (plums are fruit)
Use the results of the survey below to find each conditional probability.
How Many Pets to you have in your home?
0 Pets
1 Pet
Males
5
10
Females
4
13
15. P(male | 2 pets)
2 Pets
5
6
16. P(2 pets | male)
3+ Pets
2
2
17. P(0 pets | female)
18. Which of these is equal to 0.18 according to the tree diagram? Circle the correct answer.
.7
C
A
.3
.6
.4
A. P(C | A)
B. P(C and B)
C. P(D | C)
D. P(A and D)
D
.7
C
.3
D
B
Use the following set of values for Exercises 19 - 20.
3, 2, 3, 4, 7, 5, 6, 8, 3, 8, 2
19. Find the mean, median, and the mode(s) of the data set. Round answers to the nearest tenth, if necessary.
Mean _________
Median _________
20. Draw a box-and-whisker plot.
Mode_______
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Use the following set of values for Exercises 21 – 23.
13, 11, 15, 9, 17, 13, 15, 28, 20, 14
21. Find the range.
22. Find the values at the 40th and 90th percentiles. (40% times # of entries. 60% percentile is (.6)(10) = 6th term)
40th percentile __________
90th percentile ___________
23. Find the mean and the standard deviation. Round to the nearest tenth, if necessary.
mean = ___________
standard deviation = ____________
24. A set of values has a mean of 34 and a standard deviation of 4. Find the z-score of the value of 26.
Z-score = (value – mean) / (standard deviation)
Find the sample proportion. Write it as a percent.
25. 34 out of the 786 pairs of shoes at the shoe store were defective.
26.
A survey was taken and 18% of 350 students like school food.
a. Find the margin of error for each sample. (Round to nearest whole percent.)
b. Then find an interval that is likely to contain the true population proportion.
27. Choose the pool that is the least biased. Circle the correct answer.
A. A student stands outside an expensive restaurant and asks customers whether they are for or against welfare.
B. A magazine for bird lovers asks subscribers how many cats they own.
C. A researcher asks students in Hawaii whether they own snowmobiles.
D. A researcher stands outside a grocery store and asks shoppers whether they spend more or less than $100/wk
on groceries.
28. A bicycle-rental store has ten bicycles available for rent. On an average day, 60% of the bicycles are rented out.
Round your answers to the nearest whole percent.
a. Find the probability that on one day only four of the ten bicycles are rented out.
b. Find the probability that on one day all ten of the bicycles are rented out.
A class of 200 students takes an exam. The students’ scores are normally distributed with a mean of 72% and
a standard deviation of 10. Find the number of students with scores in each interval.
29. between 72% and 82%
30. more than 92%