NAME:____ MAT 1014.E1 Final Exam

Winter 2022

SCORE:

NOTE: RETURN ONLY THE ANSWER SHEET AT THE END OF THIS EXAM!

1. One card is selected from an ordinary deck of 52. Find the probability

as a common fraction in simplest form for each event below:

a. a face card

b. a heart and a diamond

c. a spade card and a queen

d. a black ace or a five

e. a club, a diamond or a king

____ f. a black card or a red card

2. A bag contains 8 red, 12 white and 4 blue marbles.

If 2 marbles are

selected in succession (without replacement), find the probability as a

common fraction in simplest form that:

a.

both are blue

b.

neither is red

c.

either is red or blue

d.

first is red and second is blue

e.

second is orange

____ f.

first is red, white or blue

3.On a single roll of a pair of dice, find the probability as a common

fraction in simplest form for:

a.

obtaining a sum of six

b.

obtaining a sum less than five

c.

obtaining a sum of at least eight

____ d.

obtaining sums of seven or eleven

4. In a family with 3 children, what is the probability as a common

fraction in simplest form the following outcomes:

____ a.

Two boys and one girl

b.

At most two are girls

____ c.

At least one is a boy

d.

All three are of the same sex

5. An urn contains twenty-five balls numbered 0 through 24. A single ball

is taken from the urn; find the probability as a decimal fraction for:

a.

the number 4

b.

an even number

c.

a multiple of five

d.

a prime number

____ e.

a negative number

____ f.

a whole number

6. A quiz consists of five true-false questions:

____ a.

b.

How many elements are in the sample space for answering the quiz?

If a student answers the test FTFTF, what is the probability

that the student answered all five questions correctly?

7. The probability that the Rangers will win the pennant is 3/7.

____ a.

What are the odds against the Rangers winning the pennant?

____ b.

What is the probability for the Rangers losing the pennant?

8. Suppose it is possible for a coin to land on its edge. A valid

probability

model should account for this outcome. If we assume that the

coin is

equally likely to land heads or tails, explain why the probability for

heads (or tails) cannot be 1/2 when it is possible for the coin to land

on its edge.____________________________________________________________

9. On a lab quiz, the following scores were made: 86, 75, 80, 92, 90, 71,

80, 62, 73, 81. For this set of scores, find the following:

a. mean

____ d. range

b.

e.

median

variance

c.

f.

mode

Standard Dev.

_____10. In a class of 250 students, Suzy is ranked 15th. What is her

percentile rank to the nearest percent?

11. The mean length of a cell phone call is 1.5 minutes with standard

deviation 0.25 minutes.

Assuming that the lengths of these calls are

normally distributed, determine the following:

_____a. What percentage of the calls last more than 2 minutes?

_____b. What percentage of the calls last between 1 and 2 minutes?

____ c. What percentage of the calls last at least 2 minutes?

____ d. What percentage of the calls last less than 1.5 minutes?

12.

Professor Standard Normal gives a short daily quiz to his statistics

class. The results of the most recent quiz are shown in the table.

Mean

Median

Mode

Score

0

5

6

7

8

9

10

Frequency

1

3

5

6

4

4

2

13. Kim is ranked at the 87th percentile in her class of 300 while

Bill is ranked thirty eighth in the same class. Who ranks higher?

_________

14. Explain why it is not possible to have a percentile rank of 100.

_____________________________________________________________ ___________

15. The heights of 1000 female college students were found to be normally

distributed with a mean of 66 inches and a standard deviation of 2

inches. Determine each of the following:

a. What is the probability of a height between 66 and 70 inches?

____ b, What percentage of the heights are between 62 and 70 inches?

____ c. How many of the heights are under 70 inches?

____ d. How many are between 62 and 70 inches?

____ e. How many are less than 62 inches?

16. A fire in the basement has destroyed part of a report. One whole line

and several other areas were burned. You are asked to find the value

of the third element (?) in the table below.

Value

220

254

**____(?)

248

230

Deviation

(Deviation squared)

-15

361

+13

-5

169

25

Total

924

MAT 1014 FINAL EXAM Winter 2022 ANSWER SHEET

1. a.

6. a.

b.

b.

c.

7. a.

d.

b.

e.

8.

f.

9. a.

2. a.

b.

b.

c.

c.

d.

d.

e.

e.

f.

f.

10.

3. a.

11. a.

b.

b.

c.

c.

d.

d.

4. a.

12. a.

b.

b.

c.

c.

d.

13.

5. a.

14.

b.

15. a.

c.

b.

d.

c.

e.

d.

f.

e.

16.

NAME:

____ MAT 1014.E1 Final Exam

Winter 2022

SCORE:

NOTE: RETURN ONLY THE ANSWER SHEET AT THE END OF THIS EXAM!

1. One card is selected from an ordinary deck of 52. Find the probability

as a common fraction in simplest form for each event below:

a. a face card

b. a heart and a diamond

c. a spade card and a queen

d. a black ace or a five

e. a club, a diamond or a king

____ f. a black card or a red card

2. A bag contains 8 red, 12 white and 4 blue marbles.

If 2 marbles are

selected in succession (without replacement), find the probability as a

common fraction in simplest form that:

a.

both are blue

b.

neither is red

c.

either is red or blue

d.

first is red and second is blue

e.

second is orange

____ f.

first is red, white or blue

3.On a single roll of a pair of dice, find the probability as a common

fraction in simplest form for:

a.

obtaining a sum of six

b.

obtaining a sum less than five

c.

obtaining a sum of at least eight

____ d.

obtaining sums of seven or eleven

4. In a family with 3 children, what is the probability as a common

fraction in simplest form the following outcomes:

____ a.

Two boys and one girl

b.

At most two are girls

____ c.

At least one is a boy

d.

All three are of the same sex

5. An urn contains twenty-five balls numbered 0 through 24. A single ball

is taken from the urn; find the probability as a decimal fraction for:

a.

the number 4

b.

an even number

c.

a multiple of five

d.

a prime number

____ e.

a negative number

____ f.

a whole number

6. A quiz consists of five true-false questions:

____ a.

b.

How many elements are in the sample space for answering the quiz?

If a student answers the test FTFTF, what is the probability

that the student answered all five questions correctly?

7. The probability that the Rangers will win the pennant is 3/7.

____ a.

What are the odds against the Rangers winning the pennant?

____ b.

What is the probability for the Rangers losing the pennant?

8. Suppose it is possible for a coin to land on its edge. A valid

probability

model should account for this outcome. If we assume that the

coin is

equally likely to land heads or tails, explain why the probability for

heads (or tails) cannot be 1/2 when it is possible for the coin to land

on its edge.____________________________________________________________

9. On a lab quiz, the following scores were made: 86, 75, 80, 92, 90, 71,

80, 62, 73, 81. For this set of scores, find the following:

a. mean

____ d. range

b.

e.

median

variance

c.

f.

mode

Standard Dev.

_____10. In a class of 250 students, Suzy is ranked 15th. What is her

percentile rank to the nearest percent?

11. The mean length of a cell phone call is 1.5 minutes with standard

deviation 0.25 minutes.

Assuming that the lengths of these calls are

normally distributed, determine the following:

_____a. What percentage of the calls last more than 2 minutes?

_____b. What percentage of the calls last between 1 and 2 minutes?

____ c. What percentage of the calls last at least 2 minutes?

____ d. What percentage of the calls last less than 1.5 minutes?

12.

Professor Standard Normal gives a short daily quiz to his statistics

class. The results of the most recent quiz are shown in the table.

Mean

Median

Mode

Score

0

5

6

7

8

9

10

Frequency

1

3

5

6

4

4

2

13. Kim is ranked at the 87th percentile in her class of 300 while

Bill is ranked thirty eighth in the same class. Who ranks higher?

_________

14. Explain why it is not possible to have a percentile rank of 100.

_____________________________________________________________ ___________

15. The heights of 1000 female college students were found to be normally

distributed with a mean of 66 inches and a standard deviation of 2

inches. Determine each of the following:

a. What is the probability of a height between 66 and 70 inches?

____ b, What percentage of the heights are between 62 and 70 inches?

____ c. How many of the heights are under 70 inches?

____ d. How many are between 62 and 70 inches?

____ e. How many are less than 62 inches?

16. A fire in the basement has destroyed part of a report. One whole line

and several other areas were burned. You are asked to find the value

of the third element (?) in the table below.

Value

220

254

**____(?)

248

230

Deviation

(Deviation squared)

-15

361

+13

-5

169

25

Total

924

MAT 1014 FINAL EXAM Winter 2022 ANSWER SHEET

1. a.

6. a.

b.

b.

c.

7. a.

d.

b.

e.

8.

f.

9. a.

2. a.

b.

b.

c.

c.

d.

d.

e.

e.

f.

f.

10.

3. a.

11. a.

b.

b.

c.

c.

d.

d.

4. a.

12. a.

b.

b.

c.

c.

d.

13.

5. a.

14.

b.

15. a.

c.

b.

d.

c.

e.

d.

f.

e.

16.

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