The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.

xx |
11.6 | 8.1 | 6.6 | 3.6 | 2.6 | 2.5 | 2.6 | 0.6 |
---|---|---|---|---|---|---|---|---|

yy |
13.7 | 10.8 | 9.6 | 7.4 | 6.1 | 6.3 | 5.9 | 4.4 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places)

A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 1.9 thousand automatic weapons?

Answer = Round to 3 decimal places.

The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day.

Hour of the day | Vehicles parked (thousands) |
---|---|

9 A.M. | 6.2 |

11 A.M. | 7.5 |

1 P.M. | 7.5 |

3 P.M. | 6.5 |

5 P.M. | 3.8 |

(a) Use regression to find a quadratic model for the data. (Let *V* be the number of vehicles and *t* be the time in hours since midnight. Round the regression parameters to three decimal places.)

V =

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.

xx |
11.6 | 8.3 | 7.1 | 3.3 | 2.8 | 2.7 | 2.5 | 0.4 |
---|---|---|---|---|---|---|---|---|

yy |
13.9 | 11.2 | 9.8 | 7.1 | 6.2 | 6.5 | 6 | 4.5 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

Determine the regression equation in y = ax + b form and write it below. __________Round to 2 decimal places

A) How many murders per 100,000 residents can be expected in a state with 1.8 thousand automatic weapons?

Answer = ______ Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 10.2 thousand automatic weapons?

Answer = ______ Round to 3 decimal places.

The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the number of hours after 9AM.

Hours after 9AM |
Number of vehicles parked in thousands |

0 |
6.2 |

2 |
7.4 |

4 |
7.6 |

6 |
6.7 |

8 |
4 |

a. Find the best fit quadratic model for the data.

b. Use your model to predict the number of parked cars at 2:30PM.

c. At what time of day does the city have a maximum number of parked cars?

d. What is the maximum daily amount of parked cars?

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.

xx |
11.3 | 8.3 | 6.8 | 3.4 | 2.7 | 2.7 | 2.5 | 0.4 |
---|---|---|---|---|---|---|---|---|

yy |
13.5 | 11 | 9.6 | 6.9 | 6 | 6.4 | 5.9 | 4.1 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

Use your calculator to determine the equation of the regression line. (Round to 2 decimal places)

Determine the regression equation in y = ax + b form and write it below.

A) How many murders per 100,000 residents can be expected in a state with 2.4 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 7.3 thousand automatic weapons?

Answer = Round to 3 decimal places.

The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their cars.

Speeding Ticket | No Speeding Ticket | Total | |

Red Car | 165 | 91 | 256 |

Not Red Car | 94 | 93 | 187 |

Total | 259 | 184 | 443 |

Find the probability that a randomly chosen person:

d) Has a red car given they have a speeding ticket.

e) Has a red car and got a speeding ticket.

f) Has a red car or got a speeding ticket.

The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions,

assume these values are not changing from year to year, and that the population of the United States is 312 million

people.

Cause of Death in US

Cause | Number of deaths |
---|---|

Passenger car occupant | 13,100 |

Motorcycle driver | 4,500 |

Tornado | 553 |

Skydiving | 56 |

What is the probability that an American chosen at random died as a passenger car occupant last year?

Give your answer as a decimal with a leading 0 before the decimal, rounded to the millionths.

x |
---|

11.4 | 8.4 | 6.8 | 3.3 | 2.8 | 2.6 | 2.5 | 0.9 | |

y |

13.9 | 11.1 | 9.8 | 7 | 6.7 | 6.3 | 6 | 4.9 |

x = thousands of automatic weapons

y = murders per 100,000 residents

This data can be modeled by the equation y=0.85x+4.11. Use this equation to answer the following;

A) How many murders per 100,000 residents can be expected in a state with 2 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 7.6 thousand automatic weapons?

Answer = Round to 3 decimal places.

xx |
11.3 | 8.4 | 7.2 | 3.9 | 2.5 | 2.3 | 2.3 | 0.9 |
---|---|---|---|---|---|---|---|---|

yy |
13.8 | 11 | 10.4 | 7.3 | 6.1 | 6.3 | 5.8 | 4.8 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places)

A) How many murders per 100,000 residents can be expected in a state with 1.3 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 6.5 thousand automatic weapons?

Answer = Round to 3 decimal places.

The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day.

Hour of the day | Vehicles parked (thousands) |
---|---|

9 A.M. | 6.2 |

11 A.M. | 7.5 |

1 P.M. | 7.5 |

3 P.M. | 6.5 |

5 P.M. | 3.8 |

(a) Use regression to find a quadratic model for the data. (Let *V* be the number of vehicles and *t* be the time in hours since midnight. Round the regression parameters to three decimal places.)

V =

(b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.)

V

=

thousand

(c) At what time of day is the number of vehicles parked at its greatest?

12:26 A.M.10:06 P.M. 12:06 P.M.2:26 P.M.10:04 A.M.

The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their cars.

Speeding Ticket | No Speeding Ticket | Total | |

Red Car | 107 | 193 | 300 |

Not Red Car | 80 | 195 | 275 |

Total | 187 | 388 | 575 |

Find the probability that a randomly chosen person:

a) Has a red car.

b) Has a speeding ticket.

c) Has a speeding ticket given they have a red car.

d) Has a red car given they have a speeding ticket.

e) Has a red car and got a speeding ticket.

f) Has a red car or got a speeding ticket.

x |
---|

11.5 | 8.5 | 6.7 | 3.8 | 2.6 | 2.5 | 2.3 | 0.4 | |

y |

13.9 | 11.4 | 9.5 | 7.1 | 6.3 | 6.2 | 6.1 | 4.2 |

x = thousands of automatic weapons

y = murders per 100,000 residents

This data can be modeled by the equation y=0.86x+3.96. Use this equation to answer the following;

Special Note: I suggest you verify this equation by performing linear regression on your calculator.

A) How many murders per 100,000 residents can be expected in a state with 1.8 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 9.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day.

Hour of the day | Vehicles parked (thousands) |
---|---|

9 A.M. | 6.2 |

11 A.M. | 7.4 |

1 P.M. | 7.7 |

3 P.M. | 6.5 |

5 P.M. | 4 |

(a) Use regression to find a quadratic model for the data. (Let *V* be the number of vehicles and *t* be the time in hours since midnight. Round the regression parameters to three decimal places.)

V =

(b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.)

V

=

thousand

(c) At what time of day is the number of vehicles parked at its greatest?

10:10 P.M.

12:10 P.M.

10:04 A.M.

2:26 P.M.

12:26 A.M.

xx |
11.8 | 8.4 | 7.1 | 3.9 | 2.7 | 2.7 | 2.2 | 0.7 |
---|---|---|---|---|---|---|---|---|

yy |
14.4 | 11.1 | 9.8 | 7.4 | 6.5 | 6.3 | 5.9 | 4.3 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.87x+3.89.y=0.87x+3.89. Use this equation to answer the following;

A) How many murders per 100,000 residents can be expected in a state with 2 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 4.8 thousand automatic weapons?

Answer = Round to 3 decimal places.

**4.** The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the number of hours after 9 AM.

hours after 9 AM | Number of vehicles parked in thousands |

0 | 6.2 |

2 | 7.4 |

4 | 7.6 |

6 | 6.7 |

8 | 4 |

a. Find the best fit quadratic model for the data.

b. Use your model to predict the number of parked cars at 2:30 PM.

c. At what time of day does the city have a maximum number of parked cars?

d. What is the maximum daily amount of parked cars?

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.

xx |
11.8 | 8.5 | 6.7 | 3.8 | 2.5 | 2.8 | 2.3 | 0.7 |
---|---|---|---|---|---|---|---|---|

yy |
13.9 | 11.5 | 9.9 | 7.3 | 6.4 | 6.6 | 6.2 | 4.4 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.84x+4.15.y=0.84x+4.15. Use this equation to answer the following;

A) How many murders per 100,000 residents can be expected in a state with 7.6 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 4.1 thousand automatic weapons?

Answer = Round to 3 decimal places.

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents.

xx |
11.5 | 8.5 | 6.7 | 3.5 | 2.9 | 2.7 | 2.7 | 0.9 |
---|---|---|---|---|---|---|---|---|

yy |
14.1 | 11 | 10 | 7.3 | 6.7 | 6.4 | 6.4 | 4.7 |

Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. **Round to 2 decimal places**.

According to this model, how many murders per 100,000 residents can be expected in a state with 10.2 thousand automatic weapons? **Round to 3 decimal places**.

According to this model, how many murders per 100,000 residents can be expected in a state with 5.8 thousand automatic weapons? **Round to 3 decimal places**.

The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their cars.

Speeding Ticket | No Speeding Ticket | Total | |

Red Car | 149 | 195 | 344 |

Not Red Car | 165 | 98 | 263 |

Total | 314 | 293 | 607 |

Find the probability that a randomly chosen person:

a) Has a red car.

b) Has a speeding ticket.

c) Has a speeding ticket given they have a red car.

d) Has a red car given they have a speeding ticket.

e) Has a red car and got a speeding ticket.

f) Has a red car or got a speeding ticket.

*Write your answers in decimal form, rounded to the nearest thousandth.*

Hour of the day | Vehicles parked (thousands) |
---|---|

9 A.M. | 6.2 |

11 A.M. | 7.5 |

1 P.M. | 7.5 |

3 P.M. | 6.5 |

5 P.M. | 3.8 |

b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.)

V

=

thousand

xx |
11.9 | 8.3 | 6.9 | 3.9 | 2.7 | 2.4 | 2.1 | 0.7 |
---|---|---|---|---|---|---|---|---|

yy |
14.3 | 11.3 | 10 | 7.4 | 6.5 | 6.4 | 5.9 | 4.9 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.84x+4.23. Use this equation to answer the following;

Special Note: I suggest you verify this equation by performing linear regression on your calculator.

Use the equation with the values rounded to two decimal places to make your predictions.

A) How many murders per 100,000 residents can be expected in a state with 5.5 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?

Answer = Round to 3 decimal places.

Speeding Ticket | No Speeding Ticket | Total | |

Red Car | 132 | 168 | 300 |

Not Red Car | 147 | 127 | 274 |

Total | 279 | 295 | 574 |

Find the probability that a randomly chosen person:

a) Has a red car.

b) Has a speeding ticket.

c) Has a speeding ticket given they have a red car.

d) Has a red car given they have a speeding ticket.

e) Has a red car and got a speeding ticket.

f) Has a red car or got a speeding ticket.

*Write your answers in decimal form, rounded to the nearest thousandth.*

The table below shows the number *S*, in millions, of subscribers to DirecTV *t* years after 1995.

t = years since 1995 |
S = subscribers, in millions |
---|---|

0 | 1.20 |

4 | 6.68 |

7 | 11.18 |

9 | 13.00 |

16 | 19.89 |

19 | 20.35 |

(a) Find the equation of the regression line for *S* as a function of *t*. (Round regression line parameters to two decimal places.)

S(t) =

(b) What number does this equation give for DirecTV subscribers in 2013? (Round your answer to two decimal places. The actual number was 20.25 million.)

million

(c) Explain in practical terms the meaning of the slope of the line you found in part (a). (Round your answer to two decimal places.)

The slope means that DirecTV gained million subscribers each year.

xx |
11.3 | 8 | 6.8 | 3.9 | 2.6 | 2.4 | 2.1 | 0.3 |
---|---|---|---|---|---|---|---|---|

yy |
13.8 | 10.9 | 9.7 | 7.6 | 6.2 | 5.8 | 6.1 | 4.4 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.85x+4.07.y=0.85x+4.07. Use this equation to answer the following;

Special Note: I suggest you verify this equation by performing linear regression on your calculator.

A) How many murders per 100,000 residents can be expected in a state with 7.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 1 thousand automatic weapons?

Answer = Round to 3 decimal places.

xx |
11.6 | 8.3 | 6.9 | 3.4 | 2.3 | 2.6 | 2.3 | 0.7 |
---|---|---|---|---|---|---|---|---|

yy |
13.8 | 11 | 9.9 | 6.7 | 5.8 | 6.1 | 5.7 | 4.7 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.86x+3.89. Use this equation to answer the following;

Special Note: I suggest you verify this equation by performing linear regression on your calculator.

Use the equation with the values rounded to two decimal places to make your predictions.

A) How many murders per 100,000 residents can be expected in a state with 1.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 5.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents.

xx |
11.3 | 8.2 | 7.1 | 3.7 | 2.9 | 2.2 | 2.1 | 0.6 |
---|---|---|---|---|---|---|---|---|

yy |
13.9 | 10.7 | 10.3 | 7.2 | 6.5 | 5.6 | 5.5 | 4.6 |

Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. **Round to 2 decimal places**.

According to this model, how many murders per 100,000 residents can be expected in a state with 4.6 thousand automatic weapons? **Round to 3 decimal places**.

According to this model, how many murders per 100,000 residents can be expected in a state with 4.4 thousand automatic weapons? **Round to 3 decimal places**.

Round all answers to two decimal places.

The table below shows the number *S*, in millions, of subscribers to DirecTV *t* years after 1995.

t = years since 1995 |
S = subscribers, in millions |
---|---|

0 | 1.20 |

4 | 6.68 |

7 | 11.18 |

9 | 13.00 |

16 | 19.89 |

19 | 20.35 |

(a) Find the equation of the regression line for *S* as a function of *t*. (Round regression line parameters to two decimal places.)

S(t) =

(b) What number does this equation give for DirecTV subscribers in 2013? (Round your answer to two decimal places. The actual number was 20.25 million.)

million

(c) Explain in practical terms the meaning of the slope of the line you found in part (a). (Round your answer to two decimal places.)

The slope means that DirecTV gained million subscribers each year.

xx |
11.6 | 8 | 6.8 | 3.6 | 2.4 | 2.3 | 2.3 | 0.3 |
---|---|---|---|---|---|---|---|---|

yy |
14.1 | 10.9 | 9.7 | 7.2 | 6.1 | 6.2 | 5.7 | 4.3 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation ˆy=0.86x+4.y^=0.86x+4. Use this equation to answer the following.

A) How many murders per 100,000 residents can be expected in a state with 1.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 6.9 thousand automatic weapons?

Answer = Round to 3 decimal places.

Speeding Ticket No Speeding Ticket Total

Red Car 91 131 222

Not Red Car 189 151 340

Total 280 282 562

Find the probability that a randomly chosen person:

a) Has a red car___

b) Has a speeding ticket___

c) Has a speeding ticket given they have a red car____

d) Has a red car given they have a speeding ticket___

e) Has a red car and got a speeding ticket___

f) Has a red car or got a speeding ticket___

(Write your answers in decimal form, rounded to the nearest thousandth)

Hour of the day | Vehicles parked (thousands) |
---|---|

9 A.M. | 6.3 |

11 A.M. | 7.6 |

1 P.M. | 7.6 |

3 P.M. | 6.6 |

5 P.M. | 3.9 |

(a) Use regression to find a quadratic model for the data. (Let *V* be the number of vehicles and *t* be the time in hours since midnight. Round the regression parameters to three decimal places.)

V =

(b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.)

V

=

thousand

(c) At what time of day is the number of vehicles parked at its greatest?

2:26 P.M.10:04 A.M. 10:06 P.M.12:06 P.M.12:26 A.M.

Hour of the day | Vehicles parked (thousands) |
---|---|

9 A.M. | 6.3 |

11 A.M. | 7.6 |

1 P.M. | 7.6 |

3 P.M. | 6.6 |

5 P.M. | 3.9 |

b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.)

V

=thousand

The table below shows the number of fatal heart attacks in 19 selected European Union countries during 2014 along with the 2014 debt-to-GDP ratios for these countries in 2014. Compare the coefficients of variation and comment on your findings.

Country | Fatal Heart Attacks 2014* | Debt to GDP Ratio** | |

1 | Austria | 14,521 | 225% |

2 | Belgium | 7,792 | 327% |

3 | Czech Republic | 26,171 | 128% |

4 | Denmark | 3,943 | 302% |

5 | Finland | 10,338 | 238% |

6 | France | 33,513 | 280% |

7 | Germany | 121,471 | 188% |

8 | Greece | 12,200 | 317% |

9 | Hungary | 32,138 | 225% |

10 | Ireland | 4,283 | 390% |

11 | Italy | 69,653 | 259% |

12 | Netherlands | 8,956 | 325% |

13 | Poland | 38,642 | 134% |

14 | Portugal | 7,456 | 358% |

15 | Romania | 50,667 | 104% |

16 | Slovakia | 13,381 | 151% |

17 | Spain | 32,564 | 313% |

18 | Sweden | 12,617 | 304% |

19 | United Kingdom | 69,325 | 252% |

xx |
11.8 | 8.2 | 7 | 3.5 | 2.3 | 2.3 | 2.4 | 0.5 |
---|---|---|---|---|---|---|---|---|

yy |
13.8 | 11.1 | 10.1 | 6.9 | 6.1 | 6 | 6.2 | 4.5 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.83x+4.14. Use this equation to answer the following;

Special Note: I suggest you verify this equation by performing linear regression on your calculator.

A) How many murders per 100,000 residents can be expected in a state with 2.2 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 9.3 thousand automatic weapons?

Answer = Round to 3 decimal places.

xx |
11.3 | 8.6 | 6.9 | 3.9 | 2.8 | 2.5 | 2.1 | 0.4 |
---|---|---|---|---|---|---|---|---|

yy |
13.8 | 11 | 9.7 | 7 | 6.7 | 6.5 | 6 | 4.1 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places)

A) How many murders per 100,000 residents can be expected in a state with 1.1 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 6.1 thousand automatic weapons?

Answer = Round to 3 decimal places.

# 7

xx |
11.5 | 8.4 | 7 | 3.9 | 2.9 | 2.5 | 2.4 | 0.9 |
---|---|---|---|---|---|---|---|---|

yy |
13.5 | 11.5 | 10.2 | 7.1 | 6.5 | 6.2 | 5.9 | 4.8 |

xx = thousands of automatic weapons

yy = murders per 100,000 residents

This data can be modeled by the equation y=0.85x+4.01.y=0.85x+4.01. Use this equation to answer the following;

Special Note: I suggest you verify this equation by performing linear regression on your calculator.

A) How many murders per 100,000 residents can be expected in a state with 1.7 thousand automatic weapons?

Answer = Round to 3 decimal places.

B) How many murders per 100,000 residents can be expected in a state with 10.9 thousand automatic weapons?

Answer = Round to 3 decimal places.

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