Algebra 2 Honors Probability/Statistics Review 1. A fruit bowl

Algebra 2 Honors
Probability/Statistics Review
1. A fruit bowl consists of 4 red apples, 8 green apples, 6 (green) limes, 3 oranges, and 4 bananas.
Find the probability of:
a. Selecting a red apple and then a banana without putting the apple back in the bowl.
b. Selecting a red apple and then a piece of fruit that is not green, without replacement.
c. Selecting an orange, but since you don’t like oranges, you replace it back in the bowl
then select an apple (any color).
d. Selecting a banana, yuk, replacing it, then selecting a lime, yuk, replacing it, then
selecting an orange.
e. Apple, given that it is green
f. Orange, given that it is not an apple
2. On a two question multiple choice test (3 choices per question) what is the probability of getting.
a. One question correct
b. No questions correct
c. All the questions correct
d. At least one question correct?
3. Find the missing event with the given information
P(A or B) = .95
P(A or B) = .80
P(A | B) = _______
P(A) = .70
P(A) = .60
P(B) = .4
P(B) = . 45
P(B) = _______
P(A and B) = .08
P(A and B) = _______
P(A and B) = .15
P(B | A) = .88
P(A) = .3
P(A and B) = _______
4. The mean score on the ACT in 2014 was 21 (approximation) with a standard deviation of 4.
Using the Empirical Rule determine the following. Assume the distribution is normally distributed.
a. What would be the scores of 95% of the students who took the ACT in 2014?
b. What is the minimum score of the top 16% of those who took the test?
c. What percent of the population scored less than 17 and 25?
5. When using the empirical rule if:
a. If 95% of the population score between 100 and 140 what is the mean and standard deviation?
b. If the mean score is 110, and 99.7% of the population scores 65 to 155, what is the
standard deviation?
c. If 95% of the population scores between 200 and 280, what is the mean?
6. The mean income of all subscribers to a particular magazine is $26000. We draw a random sample
of 100 subscribers and find that their mean income is $27300. Identify the
a. population
b. sample
c. parameter
d. statistic
7. The average GPA for all female volleyball players in a particular college is 2.8, and their mean height
is 182cm. Identify the parameter or statistic if there is any.
8. Determine whether the numerical value is a parameter or a statistics (and explain):
a) A recent survey by the alumni of a major university indicated that the average salary of 10,000
of its 300,000 graduates was $125,000.
b) The average salary of all assembly line employees at a certain car manufacturer is $33,000.
c) The average late fee for 360 credit card holders was found to be $56.75
9. Are the following mutually exclusive? Explain.
a) Purchasing a pet that is a dog and a cat.
b) Having a GPA of a 1.5 and getting into the University of Florida
c) Being a female who is a race care driver
d) Walking on the beach and getting stung by a jelly fish.
10. Are the following independent or dependent? Explain.
a) Rolling doubles on a pair of dice and selecting a heart from a deck of card.
b) Selecting 2 cards and getting an Ace of spades on the second pick.
c) Flipping a coin, and getting heads twice.
11. Are the following bias or unbias? Explain
a) Asking students in an Algebra II class if the teacher should give you the answers to the next test?
b) Surveying voters about increasing taxes to improve the schools.
c) Surveying a random set of adults on their favorite place to vacation.
12. 65 girls are on a field trip to a museum. 10 of the 32 sophomores play soccer. There are 28 girls
on the soccer team. How many girls are not on the soccer team?
13. Several students were surveyed. 29 students stated that they like their English teacher the best. 44
like their history teacher the most. 12 of the students stated they like their English and their history
teacher equally! If 13 students prefer a teacher other than their English and history teacher, how
many students were in the survey?
14. Universe = { the alphabet }
Set A = {A, D, G, J, M, P, S, V, Y}
Set B = {A, C, E, G, I, K, M, O, Q, S, U, W, Y}
Find the following:
a. ~ A ! B b. A ! B c. ~ A ! B d. ~ A ! B e. ~ A ! B
(
)
(
)
15. Use the z-score table to find:
a. P(z < 1.35)
b. P(z > 2.33)
c. P(-1.47 < z < 1.87)
d. P(z < -2.62)
e. P(z > -.45)
f. P(-2 < z< 1.65)
th
g. z-score for the 60 percentile
h. z-score for the top 15%
16. The mean shoes size for men is a 9, with a standard deviation of 1, while the mean shoe size for
women is an 7.5, with a standard deviation of .5. If Sarah wears a size 9 shoe, and Tom wears a
size 11, who has a bigger foot relative to their gender? Explain why.
17. The average cost of car insurance for teenagers is $143 a month, with a standard deviation of $17.
a. If a teenager is randomly selected what is the probability his insurance will be
between $1440 and $2100 a year?
b. How much does a teenager pay per month, if the price corresponds with a z score of 2.5?
18. The Stanford-Binet, used to test IQ’s, is a standardized test, meaning that norms were established
during the design phase of the test by administering the test to a large, representative sample of the
test population. The test has a mean, or average, standard score of 100 and a standard deviation of
15. Assume the distribution is normal. Membership into Mensa requires a minimum score of 132.
a. What percentage of the population meet the requirements for membership?
b. If all 4500 students at Cypress Bay were tested, how many students can we predict will qualify
for this organization?
Answers
1a. .0267 1b. .0667 1c. .0576 1d. .004608 1e. .571 1f. .231
2a. 4/9 2b. 4/9 2c. 1/9 2d. 5/9
3a. .20 3b. .35 3c. .2 3d. .264
4a. 13 – 29 4b. above a 25 4c. 68%
5a. mean = 120 standard deviation = 10 5b. 15 5c. 240
6a. all subscribers to the particular magazine b. 100 randomly selected subscribers c. $26000 d. $27300
7. 2.8 and 182cm are both parameters.
8a. Statistic – it survey of some of the graduates.
8b. Parameter – it was a survey of all graduates
8c. Statistic – it survey of some of the card holders
9a. Yes, there an animal is either a cat or a dog, not both
9b. Yes, students entering UF are required to have a higher GPA
9c. No, there are female race car drivers
9d. No, it could happen
10a. Independent - dice rolls do not affect what is drawn from a deck of cards
10b. Dependent if the card is not replaced, because – second card will be affected by the first selection.
Independent if the first card is replaced.
10c. Independent – second flip not affected by the first.
11a. bias
11b. bias
11c. unbias
12. 37
13. 98
14a. {B, F, H, L, N, R, T, Z}
14b. {A, G, M, S, Y}
14c. {C, E, I, K, O, Q, U, W}
14d. {A, B, C, E, F, G, H, I, K, L, M, N, O, Q, R, S, T, U, W, X, Y, Z}
14e. {A, B, C, D, E, F, H, I, J, K, L, N, O, P, Q, R, T, U, V, W, X}
15a. .9115
15b. .0099 15c. .8985 15d. .0044
15e. .6737
15f. .9277
15g. z-score of .23
5h. z-score of 1.04
16. Sarah does because Tom is 2 standard deviations above the mean, and Sarah is 3 standard deviations above
17a. 88.14% 17b. $185.50
18a. .0166 18b. 74.7, so approximately 75 people.