Stats Standard Number 4- Practice Worksheet

stats standard number 4- practice worksheet

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____1.The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a female student selected at random is left-handed. Express your answer as a fraction in simplest form.

Left-handed / Right-handed
Male / 2 / 35
Female / 6 / 36
a. / / c. /
b. / / d. /

____2.The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a left-handed student selected at random is female.

Left-handed / Right-handed
Male / 4 / 38
Female / 5 / 32
a. / / c. /
b. / / d. /

____3.The table shows the distribution of the labor force in the United States in the year 2000. Suppose that a worker is selected at random. Find the probability that a female works in the Industry field. Express your answer as a decimal, and round to the nearest thousandth.

Agriculture / Industry / Services
Male / 3,132,000 / 25,056,000 / 50,112,000
Female / 667,000 / 8,004,000 / 57,362,000
a. / 0.141 / c. / 0.121
b. / 0.242 / d. / 0.312

____4.Joyce asked 50 randomly-selected students at her school whether they have one or more brothers or sisters. The table shows the results of Joyce’s poll.

Make a table of the joint and marginal relative frequencies. Express percentages in decimal form.

a. /
b. /
c. /
d. /

____5.In recent years, the three most popular car colors in the United States have been black, silver, and white. Suppose a poll of 40 randomly-selected car buyers gave the following results. The table shows how men’s and women’s preferences differed in the poll.

Make a table of the joint and marginal relative frequencies. Express percentages in decimal form.

a. /
b. /
c. /
d. /

____6.A poll of 100 senior citizens in a retirement community asked about the types of electronic communication they used.The table shows the joint and marginal frequencies from the poll results.

If you are given that one of the people polled uses text messaging, what is the probability that the person is also using e-mail? Express your answer as a decimal. If necessary, round your answer to the nearest hundredth.

a. / 0.65
b. / 0.61
c. / 0.8
d. / 0.13

____7.At a small high school, there are 80 girls in the senior class. Some of them play basketball, some play soccer, some play both, and some play neither. The table shows the joint and marginal frequencies for the senior girls.

If you know that a girl plays soccer, what is the probability that she also plays basketball? Express your answer as a decimal. If necessary, round your answer to the nearest hundredth.

a. / 0.08
b. / 0.23
c. / 0.43
d. / 0.3

____8.A study compared the on-time performance for three bus companies. A table with the joint and marginal frequencies of the results is shown.

Determine which company has the best on-time performance. Explain how to identify the company that performed best.

a. / Red Dog Transit has the best on-time performance; Divide the joint relative frequency of on-time arrival by the marginal relative frequency to find the best performance.
b. / Cross-Country Bus has the best on-time performance; Identify the greatest joint relative frequency of on-time arrivals to find the best performance.
c. / Express Way Lines has the best on-time performance; Divide the joint relative frequency of on-time arrival by the marginal relative frequency to find the best performance.
d. / Cross-Country Bus has the best on-time performance; Divide the joint relative frequency of on-time arrival by the marginal relative frequency to find the best performance.

____9.Frieda made the following two-way table about the color and size of the marbles in a bag.

Blue / Red / Clear / Total
Small / 21 / 17 / 32 / 70
Large / 4 / 2 / 7 / 13
Total / 25 / 19 / 39 / 83

What is the probability that one of Frieda’s marbles is red, given that it is large?

a. / 0.154 / c. / 0.229
b. / 0.105 / d. / 0.157

____10.Jacinto made the following two-way table about whether the other students in his statistics class have siblings or pets.

Has One or More Siblings / Has No Siblings / Total
Has One or More Pets / 13 / 7 / 20
Has No Pets / 10 / 4 / 14
Total / 23 / 11 / 34

What is the probability that one of Jacinto’s classmates has a pet, given that the classmate does not have a sibling?

a. / 0.324 / c. / 0.350
b. / 0.636 / d. / 0.588

____11.Tanisha made the following two-way table about the color and pattern of the socks she owns.

White / Yellow / Red / Total
Patterned / 4 / 6 / 10 / 20
Solid / 16 / 6 / 2 / 24
Total / 20 / 12 / 12 / 44

What is the probability that one of Tanisha’s socks is patterned, given that it is red?

a. / 0.200 / c. / 0.455
b. / 0.833 / d. / 0.273

____12.The table below shows the number of days that a meteorologist predicted it would be sunny, and the number of days it was sunny. Based on the data in the table, what is the conditional probability that it will be sunny on a day when the meteorologist predicts it will be sunny?

Sunny / Not Sunny / Total
Predicts sunny / 570 / 20 / 590
Does not predict sun / 63 / 347 / 410
Total / 633 / 367 / 1000
a. / 57%
b. / 59%
c. / 90%
d. / 97%

____13.120 students are surveyed about their pets, and the results are recorded in the table. Let event be a male student being selected and event be a student with at least one pet being selected. Based on the table, are these events independent? Why or why not?

Male / Female / Total
At least 1 pet / 54 / 36 / 90
No pets / 18 / 12 / 30
Total / 72 / 48 / 120
a. / Yes, because .
b. / Yes, because .
c. / No, because .
d. / No, because .

Multiple Response

Identify one or more choices that best complete the statement or answer the question.

____14.Angela has a pack of 40 cards: some red, some blue, some with letters, and some with numbers. Based on the data shown in the table, which statements are true?

Red / Blue / Total
Number / 10 / 4 / 14
Letter / 10 / 16 / 26
Total / 20 / 20 / 40
a. /
b. /
c. /
d. /
e. / Picking a numbered card and picking a red card are independent events.
f. / Picking a lettered card and picking a blue card are independent events.

Numeric Response

15.The table shows the books in Ana’s bookcase. If she takes a paperback book from her shelf without looking, find the probability that it is a mystery. Express your answer as a decimal rounded to the nearest hundredth.

Paperback / Hardbound
Nonfiction / 30 / 31
Mystery / 39 / 37
Romance / 33 / 42

Short Answer

16.Yoshimi collected the following data about where students in different classes sat during lunch one day. The four classes are freshmen, sophomores, juniors, and seniors, and they sat either in the cafeteria or outside.

- There are 1760 students in all. There are 355 freshmen and 505 juniors.

- 235 seniors ate in the cafeteria and 280 seniors ate outside.

- 135 freshmen, 155 sophomores, and 260 juniors ate outside.

If possible, complete the two-way table using the data. If it is not possible to complete the table, fill in as much of it as you can.

Freshmen / Sophomores / Juniors / Seniors / Total
Cafeteria
Outside
Total

17.Jenna collected the following data about what kinds of food and drink students received in the cafeteria for lunch. On that day, students could choose milk, juice, or water for a drink, and chicken, pizza, or a hamburger for food.

- 755 students got cafeteria meals. All students got one type of food and one drink.

- 120 students had water, and 275 had juice.

- 195 students had chicken, and 265 had pizza.

- Of the students who had chicken, 75 had milk and 45 had juice.

- Of the students who had hamburgers, 115 had milk.

If possible, complete the two-way table from this data. If it is not possible to complete the table, fill in as much of it as you can.

Chicken / Pizza / Hamburger / Total
Milk
Juice
Water
Total

18.A frequency table of sophomores and juniors taking an SAT preparation course at Jackson High School is shown.

Taking the Course / Not Taking the Course / Totals
Sophomores / 0.1 / 0.3 / 0.4
Juniors / 0.2 / 0.4 / 0.6
Totals / 0.3 / 0.7 / 1

Are sophomores or juniors more likely to take the course? Explain your reasoning.

19.A city voted on a resolution to build a parking garage downtown. Of the voters who live less than 2 miles from downtown, 780 voted “yes” for the garage and 2,210 voted “no” for the garage. Of the voters who live 2 or more miles from downtown, 1,690 voted “yes” for the garage and 1,820 voted “no” for the garage.

Part A: Make a two-way frequency table to represent the data.

Part B: If a person voted yes for the garage, are they more likely to live less than 2 miles form downtown or 2 or more miles from downtown? Explain your reasoning.

20.The table represents the results of a survey asking high school students whether they watch sports or watch movies for entertainment.

Watches Sports / Doesn’t Watch Sports
Watches Movies / 46 / 27
Doesn’t Watch Movies / 62 / 26

Part A: What is the probability of randomly choosing a student who doesn’t watch movies? Round your answer to the nearest hundredth.

Part B: What is the probability of randomly choosing a student who doesn’t watch movies given that the student doesn’t watch sports? Round your answer to the nearest hundredth.

Part C: If you know a student doesn’t watch sports, is it more or less likely that student also doesn’t watch movies than a student selected at random? Explain.

21.The table represents the results of a survey asking members of a health club if they run or bike for exercise.

Runs / Doesn’t Run / Totals
Bikes / 27 / 73
Doesn’t Bike / 62
Total / 161

Part A: Complete the table.

Part B: What is the probability of randomly choosing a person who doesn’t bike? Round your answer to the nearest hundredth.

Part C: What is the probability of randomly choosing a person who doesn’t bike given that the person doesn’t run? Round your answer to the nearest hundredth.

Part D: If you know a person doesn’t run, is it more or less likely that person also doesn’t bike than a person selected at random? Explain.

22.Sandra is planning a dinner party for 100 people. Out of 45 men coming to the party, 36 ordered chicken. Out of the 55 women coming to the party, 24 ordered fish.

a.Complete the two-way table below.

Chicken / Fish / Total
Man / 36
Woman / 24
Total

b.What is the conditional probability that a guest who ordered fish is a man? Round to the nearest hundredth.

c.What is the conditional probability that a guest who ordered chicken is a woman? Round to the nearest hundredth.

23.Two hundred people were chosen to participate in a study involving a new cold medication.

1.55% of the people were given the medication; the rest were given a placebo.

2.After one week, 30% of the people given the medication reported having symptoms, and 50% of the people given the placebo reported having no symptoms.

Complete the two-way table below to organize the data. Are taking the medicine and not showing symptoms a week later independent events? Explain.

Medicine / Placebo / Total
Symptoms
No
Symptoms
Total

24.It is known that 3% of a population has a certain allergy. A test correctly identifies people with the allergy (positive result) 97% of the time. The test also correctly identifies people without the allergy (negative result) 94% of the time.

a.The allergy test is given to 1000 people. Use the given information to fill in the table. Round to the nearest person.

Has allergy / Does not have allergy / Total
Tests positive
Tests negative
Total / 30 / 1000

b.What is the probability that a person has the allergy if the person tests positive? Round to the nearest hundredth.

Problem

25.Jamal and Susan survey 100 students from each grade about whether they prefer math, science, English, or history.

Grade 9: 25 prefer math, 20 prefer science, 37 prefer English, 18 prefer history

Grade 10: 28 prefer math, 22 prefer science, 25 prefer English, 25 prefer history

Grade 11: 30 prefer math, 23 prefer science, 20 prefer English, 27 prefer history

Grade 12: 27 prefer math, 28 prefer science, 25 prefer English, 20 prefer history

a.Complete the two-way table below to organize the data.

Math / Science / English / History / Total
Grade 9
Grade 10
Grade 11
Grade 12
Total

b.Estimate the probability that a randomly selected student from the school prefers math.

c.Estimate the conditional probability that a randomly selected student who prefers science is in grade 12. Round to the nearest thousandth.

26.Manuela and Stephen survey 250 people at a sporting event and ask if they prefer hamburgers or hot dogs, and if they prefer regular or diet soda.

90 people said they prefer hamburgers and regular soda.

40 people said they prefer hamburgers and diet soda.

70 people said they prefer hot dogs and regular soda.

50 people said they prefer hot dogs and diet soda.

a.Complete the table to organize the data.

Regular
soda / Diet
soda / Total
Hamburger
Hot dog
Total / 250

b.What is the probability that someone who prefers diet soda will also prefer hamburgers?

c.What is the probability that someone who prefers hot dogs will also prefer regular soda?

d.Are preferring diet soda and preferring hamburgers independent events? Explain.

e.Are preferring regular soda and preferring hot dogs independent events? Explain.

Essay

27.The cars on a dealer's lot are distributed as follows.

Full Size / Mid-Size / Compact / Sub-Compact
American / 12 / 18 / 15 / 5
Japanese / 9 / 21 / 12 / 6
European / 8 / 12 / 6 / 4

For a single car chosen at random from the cars on this dealer's lot, let A be the event that the car chosen is American and B be the event that the car chosen is compact.

Part A: For a single car selected from this dealer's lot, find P(A) and . Explain your answers.

Part B: Are A and B independent events? Explain.

Part C: Estimate the probability that the next three cars sold from this lot are compact American cars?

Part D: Are the sales in Part C independent or dependent events? Explain.

Part E: Given A is the event that the car chosen is American, give an example of an independent event C.

28.An airline offers snacks to their passengers for sale during flights. They keep track of whether customers in an aisle, middle, or window seat buy the snacks or not.

Aisle Seat / Middle Seat / Window Seat / Totals
Buys a Snack / 172 / 135 / 152 / 459
Does not Buy a Snack / 516 / 405 / 456 / 1377
Totals / 688 / 540 / 608 / 1836

Compare the probabilities that passengers buy snacks given that they are sitting in an aisle seat, a middle seat, and a window seat. Can you determine whether buying a snack and seat location are independent or dependent events? Explain why or why not.

Other

29.A bag contains green, orange, and purple balls, each numbered with a 1 or a 2. The table below shows how many of each kind of ball are in the bag. Classify each pair of events as independent or not independent.

1 / 2 / Total
Green / 8 / 7 / 15
Orange / 9 / 6 / 15
Purple / 7 / 3 / 10
Total / 24 / 16 / 40
a. Picking a green ball and a ball with a 1 on it / Independent / Not independent
b. Picking an orange ball and a ball with a 1 on it / Independent / Not independent
c. Picking a purple ball and a ball with a 1 on it / Independent / Not independent
d. Picking a green ball and a ball with a 2 on it / Independent / Not independent
e. Picking an orange ball and a ball with a 2 on it / Independent / Not independent
f. Picking a purple ball and a ball with a 2 on it / Independent / Not independent

stats standard number 4- practice worksheet

Answer Section

MULTIPLE CHOICE

1.ANS:BPTS:1NAT:NT.CCSS.MTH.10.9-12.S.CP.4

TOP:Find Probabilities of Independent and Dependent EventsKEY:conditional | probability

DOK:DOK 1

2.ANS:BPTS:1NAT:NT.CCSS.MTH.10.9-12.S.CP.4

LOC:MTH.C.13.05.03.016TOP:Find Probabilities of Independent and Dependent Events

KEY:conditional | probabilityDOK:DOK 1

3.ANS:CPTS:1REF:179e4fea-4683-11df-9c7d-001185f0d2ea

OBJ:Using a Table to Find Conditional Probability

NAT:NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.CP.6 | NT.CCSS.MTH.10.9-12.S.CP.8

LOC:MTH.C.13.05.03.016TOP:Independent and Dependent Events

DOK:DOK 2

4.ANS:CPTS:1REF:906d9aa8-6ab2-11e0-9c90-001185f0d2ea

OBJ:Finding Joint and Marginal Relative Frequencies

NAT:NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.ID.5