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**Focus Set 3 â€“ Fundamental Counting Principle**

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Provide answers to **# 1 - 10** below.

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**Show how you set up your problem and then do the math.**

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1.Â If there are four roads from town A to town B and three roads from town B to town C, how many routes are there from town A to town C which go through town B?

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2. Â How many different 4-letter radio station call codes are possible if each code must begin with K or W and no letter can be repeated? Â Examples:Â WABC, KABC, or WABK

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3.Â A firm wants to assign its employees ID numbers that have say* x* digits each. If a firm has 800 employees, what is the **smallest number of digits** (that is, the smallest *x*) that the firm can use for eachÂ ID number? Assume that repetition of digits is permitted.Â Â

(Hint: There is no formula for this â€“ you just have to reason it out, but you must be enough ID's to go around!)

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4.Â In how many ways can 10 questions on a True-False test be answered?

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5.Â In how many ways can a president and vice president be selected from a club consisting of Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12 people?Â

(Assume that these 2 positions cannot be occupied by the same person.)

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6.Â In how many ways can 5 people be seated in a row?

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7.Â How many ways can 6 people be seated in a row, if Ruth must be seated in the first chair?

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8.Â How many distinct ordered arrangements can be made with the letters of the word TENNESSEE?

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9.Â You are trying to schedule classes for next semester and wish to enroll in Math, English, Fine Arts, and History.Â Â You have found 4 Math sections, 5 English sections, 6 Fine Arts sections, and 2 History sections that do not have conflicts.

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How many different possible schedules can you develop using these options? Â

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10.Â It is lunchtime and you wish to build a pizza with 1 choice of crust, 1 meat, 1 vegetable.Â Â

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You have the following choices:Â 2 types of crust, 4 types of meats, and 7 types of vegetables

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Â How many different ways can you build your pizza?

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**Focus Set 4 â€“ Permutations and Combinations**

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**Use your calculator to solve the following problems:**

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1.Â Â Â 12!

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Â Â Â Â Â Â Â 8!

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2.Â Â P(5,3)

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3.Â Â C(5.3)

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**For # 4-8, show how you set up your problem and then do the math.**

Use your calculators to find Combinations and Permutations.

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4.Ms. Leeâ€™s class is having a spelling contest.Â There are 4 finalists in the contest.

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Â Â Â Â Â How many different ways can the 4 students be seated on the stage?

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5.Â A Book Store wishes to display five books in the window of the shop.Â Â They want to choose 5 mystery books from a list of 12 new mystery books.Â

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Â Â Â Â Â How many ways can this be done?Â (order is not important)

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6.Â On an English test, Jeff must write an essay for three of six questions in Part 1, and two of five questions in Part 2. How many different combinations of questions can be chosen?

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7.Â A club is selecting a program committee.Â They want to select 5 people from their membership of 20 people.Â Â How many ways can this committee be formed?

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8.Â Â A committee at of 5 is to be formed from a group consisting of 8 Democrats, 7 Republicans, and 2 Independents.Â **Note:** A committee is an *unordered* group.

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(a) How many committee choices are possible if the committee is to consist entirely of Democrats?

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(b) How many committee choices are possible if the committee is to consist of 2 Democrats, 2 Republicans, and 1 Independent?

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(c)Â How many committee choices are possible if the committee is chosen from all 17 people with no restrictions?

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**Focus Set 5 â€“ Introduction to Probability and Odds**

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**Write probabilities as fractions reduced to lowest terms or decimals rounded to 3 decimal places.**

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1.Â If you write the numbers **0, 1, 2, 3, 4, 5, 6, 7, 8, **and**Â 9** on slips of paper and

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place them in a hat, then you draw one slip of paper.Â

(Note: There are 10 slips of paper.)

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What is the probability of dawning the following:

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a)Â Â Â Â Â Â Â Â a number greater than 7? P(x > 7)

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b) Â Â Â Â Â Â Â a number less greater than 4 and less than 8?Â P(x>4 and x<8)

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2. A single card is dealt from a standard deck of 52 cards. What is the probability that:

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(a) Â Â Â Â Â the card is a club? Â

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(b)Â Â Â Â Â Â the card is a picture card?

(Picture cards have faces.Â Aces are not picture cards.)

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Â |
Â Â Â Â A |
Â Â Â Â Â B |
Â Â Â Â Â C |
Â Â Â Â D |
Â Â Â Â F |

Freshmen |
Â Â Â Â 2 |
Â Â Â Â Â 5 |
Â Â Â Â Â 10 |
Â Â Â Â 6 |
Â Â Â Â 5 |

Sophomores |
Â Â Â Â 3 |
Â Â Â Â Â 6 |
Â Â Â Â Â 9 |
Â Â Â Â 2 |
Â Â Â Â 2 |

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3. The grade distribution for a particular finite math class (not mine) populated by freshmen and sophomores is as shown in the table.

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Suppose we randomly select a student from this class.

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(a) What is the probability that the student made a D?

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(b) What is the probability that the student is a freshman?

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**Odds ****should be written as ratios.**

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**Probabilities**** should be as fractions or decimals.**

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Fraction must be in lowest terms.

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Decimals must be rounded to 3 decimal places.

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4. A single card is selected from a standard deck of 52 cards.

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a)Â Â Â Â Â Â Â Â What are the *odds in favor* of selecting an

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b) Â Â Â Â Â Â Â What are the *odds against*selecting a

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5. If the odds against Andre winning his tennis match are 4**:**5, then what is the ** probability **that Andre will win his tennis match?

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6. If the odds in favor of an event are 2**:**5, then what is the ** probability** that the event will occur?

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**Focus Set 6 â€“ AND and OR Probability**

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**Write probabilities as fractions or decimals. All fractions MUST be reduced to lowest terms. All decimal MUST be rounded to 3 decimal places.**

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1. A single card is dealt from a standard deck of 52 cards. What is the probability that:

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(a) the card is a 5 **and** club ?

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(b) the card is a diamond **or** King?

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(c) the card is a 5 **or** a 2?

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(d)Â the card is a 5 **and** a 2?

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Â |
Â Â Â Â A |
Â Â Â Â Â B |
Â Â Â Â Â C |
Â Â Â Â D |
Â Â Â Â F |

Freshmen |
Â Â Â Â 2 |
Â Â Â Â Â 5 |
Â Â Â Â Â 10 |
Â Â Â Â 6 |
Â Â Â Â 5 |

Sophomores |
Â Â Â Â 3 |
Â Â Â Â Â 6 |
Â Â Â Â Â 9 |
Â Â Â Â 2 |
Â Â Â Â 2 |

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(e) the card is a diamond **or** a picture card?

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(f)Â the card is a diamond **and** a picture card?

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2. The grade distribution for a particular finite math class (not mine) populated by freshmen and sophomores is as shown in the table.

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Suppose we randomly select a student from this class.

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(a) What is the probability that the student is a freshman **and **made a D?

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(b) What is the probability that the student is a freshman** or** made a D?

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(c)Â Â What is the probability that the student is a sophomore **and **made an A?

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(d)Â What is the probability that the student made a B **or** a freshman?

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**Focus Set 7 â€“ Conditional Probability & Expected Value**

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**Instructions:Â TYPE you answers after the problems. Write probabilities as fractions or decimals. All fractions MUST be reduced to lowest terms. All decimal MUST be rounded to 3 decimal places.**

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**1.Â ***One* card is drawn from a standard deck of cards. What is the probability that card is a Queen, *given that* the card is black?

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**2.Â ***One* card is drawn from a standard deck of cards. What is the probability that card is a club, *given that* the card is black?

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**3.Â ***Two *cards are drawn from a standard deck of cards *with* replacement.

What is the probability that the first is a King and the second is not a King?

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**4.Â ***Two *cards are drawn from a standard deck of cards *without* replacement. What is the probability that the first is a King and the second is not a King?

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**5.Â **The grade distribution for a particular finite math class having only freshmen and sophomores is shown in the table. Â

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Â |
A |
B |
C |
D |
F |
Totals |

Freshmen |
2 |
5 |
10 |
6 |
5 |
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Sophomores |
3 |
6 |
9 |
2 |
2 |
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Totals |
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a)Â Â Â Â Â Â Â Â What is the probability that the student made an C?

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b)**Â Â Â Â Â Â Â **What is the probability that the student is a sophomore?

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c)Â Â Â Â Â Â Â Â What is the probability that the student made a C, *given that* the student is a sophomore?Â Â This isÂ Â P( C** |** sophomore )

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d)** Â Â Â Â Â Â Â **What is the probability that the student is a freshman, *given that* the student

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Â Â Â Â Â Â Â Â Â Â Â made a B?Â Â This isÂ Â P( Freshman** |** B)

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6. An insurance company is going to sell 1-year life insurance policies with a face value of $40,000 to 25 year old men for $5000. Their mortality tables show that such men will live for 1 year with probability 0.90. Â Â

Find the company's expected earnings per policy.

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7.Â An outdoor spring festival is planed.Â The weatherman is predicting a 20% chance of rain, 30% chance of a cloudy day, and a 50% chance of sunshine.Â The committee feels that if it rains, then only 500 people will attend, if it is cloudy, then only 10000 will attend, and if the sunny, then 15000 will attend.Â Â How many people can be expected to attend the spring festival?

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Focus Set 8 - Statistics

Round all statistics to 3 decimal places.

1. Draw a Stem and Leaf chart for this data: Â 45, 49, 49, 49, 50, 55, 58, 60, 62, 68

Â Use the key 4 | 5 represents 45.

Draw the stem and leaf:Â

(Use the vertical bar above the Enter key to make the vertical lines)

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2.Â Which histogram best fits the following data:Â (Answer is just A, B, or C.)

DataÂ Frequency

1Â 3

2Â 5

3Â 8

4Â 4

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AÂ Â Â BÂ Â CÂ

3. a)Â Find the mid-point of the second class.

Â Â Â b)Â Find the total number of pieces of data.

DataÂ Frequency

15-18Â 6

19-22Â 10

23-26Â 12

27-30Â 4

4.Â Create a frequency chart with classes of width 5 beginning with 55 for the following data:

79Â 62Â 87Â 84Â 55Â 76Â 67Â 73Â 82Â 68Â

82Â 76Â 56Â 79Â 61Â 64Â 64Â 67Â 79Â 68

Â I have created a table where you can insert your classes and frequencies by just clicking and typing.Â If you need more boxes just press TAB to get more lines.Â

DataÂ Â

ClassesÂ Frequency

55 -Â Â

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**Focus Set 9 â€“ Statistics**

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**Â Round all statistics to 3 decimal places.**

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- Find the following statistics using this data:

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**Â Â 152Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 162Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 174Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 179Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 185Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 185Â Â Â Â **

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**Â Â 152Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 163Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 176Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 180Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 185Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 192Â Â Â Â **

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**Â Â 156Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 165Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 176Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 183Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 185Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 192****Â Â Â Â **

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mean =Â **Â **

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median =Â

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mode =Â **Â **

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midrange =Â

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standard deviation =Â **Â **

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range =Â **Â **

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Â 2.Â Â Â Â Â Â Find the following statistics using this data:

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**Â Â 53Â Â Â Â Â Â Â 63Â Â Â Â Â Â Â 75Â Â Â Â Â Â Â 80Â Â Â Â Â Â Â 82Â Â Â Â Â Â Â 92**

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**Â Â 56Â Â Â Â Â Â Â 68Â Â Â Â Â Â Â 75Â Â Â Â Â Â Â 82Â Â Â Â Â Â Â 82Â Â Â Â Â Â Â 92**

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**57Â Â Â Â Â Â Â 70Â Â Â Â Â Â Â 77Â Â Â Â Â Â Â 82Â Â Â Â Â Â Â 85Â Â Â Â Â Â Â 95**

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**60Â Â Â Â Â Â Â 71Â Â Â Â Â Â Â 79Â Â Â Â Â Â Â 82Â Â Â Â Â Â Â 90Â Â Â Â Â Â Â 97 **

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mean =

median =

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mode =

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midrange =

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standard deviation =

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range =

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**Focus Set 10Â â€“ Normal Curves **

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**You must put the percent symbol on percentages.**

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**Round decimals to 3 decimal places before changing decimals to percents.**

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**Ex.Â Â 0.3456345 = 0.346 = 34.6%**

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**1. **On a particular section of a CPA exam for which the scores were normally distributed with a mean of 700 points and a standard deviation of 70 points**.** Â Â

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**(a)**Â What percent of the students scored lower than 640 on the exam?

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** Â (b)**Â What percent of the students scored between 630 and 730 on the exam?

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** Â (c)**Â What percent of the students scored between 600 and 700 on the exam?

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** (d)Â **What percent of the students scored above 700 on the exam?

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** (e)Â **Â If 900 people take the exam, how many people will score above 750 on the exam?

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**2****.** Â The weights of boxes of Brand Z cereal were found to be normally distributed with a mean of 22**.**0 ounces and a standard deviation of 0**.**6 ounces**.**

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**(a)** What percentage of the boxes will weigh more than 21.7 ounces?

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**(b)** What percentage of the boxes will weigh between 21.7 and 22.3 ounces?

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**(c)**Â What percentage of the boxes will weigh less than 22.5 ounces?

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**(d)Â **What percentage of the boxes will weigh more than 23 ounces?** **Â Â Â Â Â Â Â Â Â Â Â

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**(e) **If a store has 500 boxes of cereal, how manyof them will weigh more than 23 ounces?

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Subject | Mathematics |

Due By (Pacific Time) | 09/16/2014 12:00 pm |

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