For Problems 1-4 refer to the following information.

A government testing agency routinely tests various items to ensure that they meet label requirements.  Fourteen 100-centiliter bottles of water were randomly selected from The Beverage Company.  Those bottles actually contained the following amounts, rounded to the nearest centiliter.

106     94     88    103    111

99     99    102     94     89

80     79     79     99

1. Fill in the blanks.

1. The data collected is _
2. This data is ___
3. The level of measurement is ___
   .
4. _____ percent of the bottles contained under 100 cL.

2.        Construct a stem-and-leaf plot and make a statement about the shape of the distribution.

3.        Using the raw data, calculate:

1. the mean amount of water in these bottles.
2. the standard deviation of the water in these bottles.

4.        Using the raw data, calculate:

1. the modal amount of water in these bottles.
2. the interquartile range (IQR).

For Problems 5 and 6 refer to the following information.

In a survey regarding sleep, people employed in 9 A.M. to 5 P.M. jobs were asked the time they awake each weekday morning. The following information was obtained.

Time         Number of Respondents

5 up to 6 A.M. &nbs p;         6

6 up to 7 A.M.          14

7 up to 8 A.M.          27

8 up to 9 A.M.           3

5.        To construct a frequency polygon for the data above, what are the coordinates of the points that need to be plotted?

6.        Calculate:

1. the mean wake-up time.
2. the range in wake-up times.

7.        Identify the method of sampling described.  (convenience, cluster, simple random, stratified, systematic)

a)         In a large office building, 50 employees are selected by extracting their employee ID numbers from a computer generated arbitrary list.

b) Every tenth employee entering the building is asked to state at which time he/she awoke for work that morning.

8.        The average amount of 20sleep employees in 9 to 5 jobs obtain per night is 7.2 hours with a standard deviation of 0.6 hours.  The average salary of these workers is $51,000 with a standard deviation of $2,400.  Is there more dispersion in the hours of sleep obtained or in the salaries of the employees?  Support your answer with numerical evidence.

For Problems 9-11, refer to the information below.

A small real estate company that specializes in residential listings recently became interested in determining the likelihood of one of their listings being sold within a certain number of days.  An analysis of the company sales of 800 homes in previous years produced the following data.

Days Listed Until Sold

Initial Asking Price Under 30     31-90      Over 90      Total

Under $150,000          50        40           0            90

$150,000-$199,999       25        150         80           255

$200,000-$250,000       15       270        110           395

Over $250,000           10        30         20            60

Total             100       490        210           800

If a listing is randomly selected, what is the probability that

9.        it was listed for under 30 days until sold?

10.   it was listed for under 30 days until sold, given that the initial asking price was under $150,000?

11.   it was listed for under 30 days until sold or the initial asking price was under $150,000?

12.   If three dice are rolled in succession (roll one die then roll the next then roll the third die), what is the probability that all 3 land with a 5 up?

13. A standard deck of cards consists of 52 cards.  There are 13 red hearts, 13 red diamonds, 13 black clubs, and 13 black spades.  Furthermore each suit contains a 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and an ace.  The jack, queen, and king are considered face cards.  What is the probability of selecting two cards without replacement from a well-shuffle deck and the first card selected is a heart and the second card selected is red?  For this problem please first state your answer in fractional form and then either write your answer in simplified fractional form, decimal form, or percent form.

For Problems 14 and 15 refer to the following information.

A major corporation has sales branches in nine cities.  The company president wants to visit five of the cities.

14. How many different groups of five cities can be selected from the nine?

15. Once the five cities are selected, how many different itineraries are possible?

For Problems 16 and 17 refer to the following information.

An automobile insurance company has constructed the chart below, where X is the amount of the claim to the nearest $5000.

X          P(X)

$0       0.70

$5000       0.25

$10000       0.05

16. Find the mean average claim amount.

17. Find the standard deviation of this distribution.

For Problems 18-21, refer to the following information.

Packages that contain one tiny pot with one Venus Fly Trap seed inside can be found for sale in the Toy Department of a BX.  Included in the package is a notice regarding the germination rate.  Let’s use 80% as the germination rate (this is rounded from what is actually stated in the packages) and let’s assume that this is a promotional offer so this BX only obtained a shipment of 20 of these packages.

18.         What is the expected number of seeds to germinate in this shipment? AND what is the standard deviation?

19.  What is the probability that a seed will not germinate?

20.  What is the probability that more than 16 or 17 of the seeds in this shipment germinate?

21.  Let’s say that due to popular demand, the BX orders a second shipment that consists of 50 packages.

a)     If using the normal distribution to approximate the probability that more than 40 of them will germinate, then what correction must be made to the 40 in order to improve the approximation of the probability?

b)     Why can the normal distribution be used to approximate the above probability?  Support your answer with numerical evidence.

For Problems 22-24, please refer to the following information.

In an annual local competitive running event, records indicate that the average time taken by participants is 27.5 minutes with a standard deviation of 6.1 minutes.  The times appear to be normally distributed.

22. What is the probability that an individual completes the course in less than 15 minutes?

23. What is the probability that an individual takes between 20 and 30 minutes to complete the course?

24. The slowest 3% of the runners take more than what amount of time to complete the course?

25. Find:  P(z > -1.24)

26. True or False:

1. The percentages for the amount of data within 1, 2, an d 3 standard deviations of the mean according to Chebyshev’s Theorem are based upon the normal distribution.
2. If np > 5 and nq > 5 then the probabilities calculated using the normal distribution will be good approximations to the actual binomial probabilities.

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