Written Assignment on Math

The written assignment draws mostly on even-numbered exercises from the textbook. Answer all assigned exercises, and show all work.

Each problem is worth 5 points. Please show work where appropriate for full credit.

Section 12.1 Problems 6, 8, 10, 12

6. Fill in the blank with the appropriate word or phrase.

Probability determined through a study of the possible outcomes that can occur for a given experiment is called empirical probability.

8. Pair of Dice. Roll a pair of dice 60 times and record the sums. Determine the empirical probability of rolling a sum of

2.

2/60=1/30

7.

15/60=1/4

Does the probability of rolling a sum of 2 appear to be the same as the probability of rolling a sum of 7? Explain your answer.

No. to obtain a sum of seven, different outcomes could add up to it for instance 3+4, 1+6 while to obtain 2 only 1+1 could add up

10. Two Coins. Flip two coins 50 times and record the number of times exactly one head was obtained. Determine the empirical probability of flipping exactly one head. How does this compare to the theoretical probability of flipping a coin and getting heads.

Exactly one head; 34/50

Theoretically the probability of obtaining exactly one head for the 50 flips is but practically it could be less or more.

12. Music Purchases. At the Virgin Music store in Times Square, 60 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 60, 12 chose rock, 16 chose country, 8 chose classical and 24 chose something other than rock, country or classical. Determine the empirical probability that the next person entering the store favors

Rock music.

12/60=1/5

Country music.

16/60=4/35

Something other than rock, country, or classical music.

24/60=2/5

Section 12.2 Problems 14, 46, 48, 50

14. Raffle. In a raffle where one number is chosen, determine the probability that you would win if you have a choice of 52 numbers to choose from.

= 1/52

TALLAHASSEE. In Problems 46, 48 & 50, each individual letter of the word TALLAHASSEE is placed on a piece of paper and all 11 pieces of paper are placed in a ha. If one letter is selected at random from the hat, determine the probability that

46. The letter S is not selected.

p(letter s is selected)=2/11

p(letter S is not selected)= 1-2/11=9/11

48. The letter T or E is selected.

p(T)=1/11, p(E)= 2/11

p(T) or p(e)=1/11+2/11=3/11

50. The letter V is not selected.

=

Section 12.5 Problems 6, 14

6. Selecting Dates. If two dates are selected at random from the 365 days of the year, use the counting principle to determine the number of possible outcomes if the dates are selected

With replacement.

365365=133225 outcomes

Without replacement.

365364=132860 outcomes

14. Three Coins. Three coins are tossed. (hint you may want to draw a tree diagram to list the sample space.)

Determine the number of points in the sample space.

8

Determine the probability that no heads are tossed.

1/8

Determine the probability that exactly one head is tossed.

1/83=3/8.

Determine the probability that three heads are tossed.

1/8

Section 13.1 Problems 14, 16, 18, 20

In Exercises 14, 16, 18 & 20, identify the sampling technique used to obtain a sample. Explain your answer.

14. Every 10th iPod coming off an assembly line is checked for defects.

Systematic

16. A door prize is given away at a home improvement seminar. Tickets are placed in a bin, and the tickets are mixed up. Then a ticket is selected by a blindfolded person.

Random

18. The businesses in Iowa City are grouped according to type: medical, service, retail, manufacturing, financial, construction, restaurant, hotel, tourism, and other. A random sample of 10 businesses from each type is selected.

Stratified

20. The Food and Drug Administration randomly selects five stores from each of four randomly selected sections of a large city and checks food items for freshness. These stores are used as a representative sample of the entire city.

Cluster

Section 13.2 Problems 2, 4, 8

Misinterpretations of Statistics. In Exercises 2, 4 & 8, discuss the statement and tell what possible misuses or misinterpretations may exist.

2. In 2011, Liberty Travel received more requests for travel brochures to Hawaii than to Las Vegas. Therefore, in 2012, Liberty Travel sold more travel packages to Hawaii than to Las Vegas.

Many travel requests came from Hawaii but this doesnt mean the tickets sold to Hawaii were more than those to Las Vegas.

4. Healthy Snacks cookies are fat free. So eat as many as you like and you will not gain weight.

Health snacks have no fat but that doesnt mean eating much wouldnt lead to obesity as other elements in them could add weight to the consumer.

8. Arizona has the highest death rate for asthma in the United States. Therefore, it is unsafe to go to Arizona if you have asthma.

Visiting a region with high death rate for asthma would not lead to death to an asthmatic person but other factors could.

Section 13.3 Problems 32, 34, 36

32. Car Insurance. Use the histogram below to answer the following questions.

a) How many students were surveyed?

31 students

b) What are the lower and upper class limits of the first and second classes?

624.5-675.5-726.5

c) How many students have an annual car insurance premium in the class with a class mark of $752?

6 students

d) What is the class mark of the modal class?

778-729

34. San Diego Zoo. Use the frequency polygon below to answer the following questions.

a) How many families visited the San Diego Zoo four times?

8 families

b) How many families visited the San Diego Zoo at least six times?

11+9+3+1=24 families

c) How many families were surveyed?

2+4+8+8+6+11+9+3+1=52 families

36. Automobile Accessories. A sample of 600 people was asked which one automobile accessory they would most prefer to have on a family road trip. The following circle graph shows the percentage of respondents that answered GPS, DVD player, extra cup holders, roof rack and other. Determine the number of respondents for each category.

100%=360=600 respondents

GPS=29%=360*29/100=104.4; = 600104.4/360=174 respondents

DVD=27%=360*27/100=97.2; = 60097.5/360=162 respondents

Extra cup=15%=360*15/100=54; = 60054/360=90 respondents

Roof rack=8%=360*8/100=28.8; = 60028.8/360=48 respondents

Other=21%=360*21/100=75.6; =60075.6/360=126 respondents

References

Torrence, B. F., & Torrence, E. A. (2009). The student's introduction to Mathematica: A handbook for precalculus, calculus, and linear algebra. Cambridge: Cambridge University Press.