 EXAM 1

The following is a list of the Motor Vehicle Theft Rate for 25 states during 2008.

DATA:  (Motor Vehicle Theft Rate)

334.4        110.4        413.6        152.5        455.8

124.7        416.0        247.2        266.0        356.0

329.4        494.7        374.5        247.3        378.6

509.6        444.3        523.3        298.9        410.7

253.3        216.3        309.6        213.8        331.6

1)Create a frequency distribution table for the data using 6 classes beginning your first class with a lower class limit of 110 and use a class width of 70.

Also, make a column for the relative frequency and percentage.

2)   Construct a Histogram for the Relative Frequency from problem (#1).

(make sure to label both axes)

3)Using the same data as in problem #1, construct a Cumulative Frequency Distribution Table.  Also make a column for the Cumulative Relative Frequency.

4)The following gives the frequency distribution of the times (in minutes) that 50 commuter students at a large university spent looking for parking spaces on the first day of classes this Spring semester.  Determine the mean and standard deviation from the given frequency distribution table.

Class                        Frequency

0 to less than 4                        1

4 to less than 8                        7

8 to less than 12                     15

12 to less than 16                   18

16 to less than 20                    6

20 to less than 24                    3

The following sample gives the lengths of time (in weeks) taken to find a full-time job by 18 computer science majors who graduated in 2006 from a local college.

10        3        12        21        15        8        4        3        16

8        9        14        33        8        24        11        42        15

5)(a)What is the mean number of weeks taken to find a full-time job by

these college graudates?

(b)What is the median number of weeks taken to find a full-time job by

(c)What is the mode of the number of weeks taken to find a full-time job

6)What is the standard deviation of the lengths of time (data from #5)?

(assume the data values represent a sample of data values)

7)The owner of a car dealership has recorded the number of cars sold during the first 20 months that he has owned the dealership.

8        5        12        3        9        10        6        12        8        8

4        16        10        11        7        7        3        5        9        11

Consider this data to be a population.

(a)Determine the Mean amount of cars sold each month.

(b)Determine the standard deviation for this data set.

8)Using the data in problem #7, construct a Box and Whisker Plot for the data.  Make sure to include your work for the five-values!

9)Suppose that mean life of a certain brand of automotive batteries is 44 months with a standard deviation of 3 months.

(a)Find the values that mark the boundaries for the battery lives that are  within 2.4 standard deviations above and below the mean.

(b)Using Chebyshev’s Theorem, find the percentage of batteries that have a battery life between the values you found in part (a).

EXAM 2

1)In a sample of adults, some of the adults own iPods while the other adults do not.  Two of the adults from this sample are to be selected at random and it will be observed whether the person selected owns an iPod or not.

(a)Draw a tree diagram for this experiment.

(b)Write out the sample space for this experiment.

2)From the problem in #1, lets assume that there are 18 adults total in the sample and only 7 of them own iPods.

Find the probability that when two adults are selected (without replacement) from this sample that both adults own an iPod.

1. 3)    The following table gives the two-way classification of all employees of a company by gender and college degree.

Male (M)            7                                                20

Female (F)         4                                                 9

If one of these employees was selected at random, find the probability that:

(a)the employee is a Male and a College Graduate.

(b)the employee is a Female given that the employee is Not a College Graduate.

(c)the employee is a College Graduate given that the employee is Male.

(d)the employee is a Male or a Female.

4)According to a recent survey, 15% of Americans that purchase a new car will keep that car for longer than 15 years.  Suppose this result holds true for the current population of all Americans.  In this experiment two American car owners will be selected at random.  Let x denote the number of American car owners who will keep their car for longer than 15 years.

(a)Create a probability distribution table of x for this experiment.

(draw a tree-diagram to help identify all of the possible outcomes)

(b)Calculate the mean and standard deviation of this probability distribution.

5)According to a study performed in 2007, 30% of U.S. taxpayers cheat on their returns.  Suppose this is true for the current population of U.S. taxpayers.  If 10 tax returns are selected to audit at random, find the probability that at most 2 of the returns came from taxpayers that had cheated.

6)Last semester there were nine students in my Math 12 class that earned A’s for their final semester grade.  Three of those nine students had taken Math 12 a previous semester.  If I were to select four of those nine students at random, find the probability that two of the students selected had taken Math 12 previously.

7)Find the area under the standard normal curve:

(a)between  and

(b)to the right of

***write your solutions as decimals, rounded to four decimal places ***

8)Rodgers Corporation makes flashlight bulbs.  The life (period before which a flashlight bulb needs to be replaced) of a typical Rodgers bulb has a normal distribution with a mean of 70 months and a standard deviation of 8 months.

Find the probability that a randomly selected Rodgers flashlight bulb had a life of less than 48 months.

9) If is known that the life of a calculator manufactured by DuraCalc has a normal distribution with a mean of 64 months and a standard deviation of 6 months.  What should the warranty period be to replace a malfunctioning calculator if the company does not want to replace more than 2% of all the calculators sold?

10)A point guard playing for Cal Berkeley was notorious for taking a long time to shoot a free throw once he was given the ball by the referee.  It was observed that the times from when he was given the ball to the time he shot the free throw were normally distributed with a mean time of 15 seconds and standard deviation of 8 seconds.  What percentage of the times were between 12 and 20 seconds?

EXAM 3

1)The average number of milligrams (mg) of sodium in a certain brand of low-salt microwave frozen dinners is 600mg.  The standard deviation for all of this brands low-salt microwave frozen dinners is 35mg of sodium.  Assume that the number of mgs of sodium in the frozen dinners is normally distributed.

(a)  If a single dinner is selected, find the probability that the sodium content will be more than 620mg.

1. (b) If a sample of 10 dinners is selected, find the probability that the mean of the sample will be larger than 620mg.

2)According to the U.S. Department of  Health and Human Services, 44% of all Americans take at least one prescription drug regularly.  Assume that this percentage is true for the current population of Americans, and let  be the proportion of Americans in a random sample of 900 who take at least one prescription drug regularly.  Find the probability that the value of  is:

(a)greater than .48

(b)between .43 and .46

3)        A random sample of 200 college students was asked if they believed that places could be haunted, and 65 of them responded yes.  Estimate the true proportion of college students who believe in the possibility of haunted places with 99% confidence.  Round your final answer to two decimal places.

4)A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of \$3987 and the population standard deviation is \$630.  Find a 90% confidence interval for the true mean yearly tuition.  Round your final answer to the nearest whole dollar.

5)From the data in problem #4 above, answer the following questions.

(a)What was the Margin of Error for the confidence interval?  (Round your answer to 2 decimal places)(b)Approximately what sample size would be needed to get the error to be \$50?

6)A recent study of 28 employees of Cabrillo College showed that the mean distance traveled to work for the sample was 14.3 miles.  The standard deviation of the sample was 2 miles.  Assume that the population of distances traveled to work is normally distributed.  Find the 95% confidence interval for the population mean distance traveled to work.  Round your final answer to the nearest tenth of a mile.

7)The American Automobile Association (AAA) claims that 54% of fatal car/truck accidents are caused by driver error.  A researcher studies 50 randomly selected accidents and finds 28 were caused by driver error.  Using the 5% significance level, test if the percentage of fatal car/truck accidents caused by driver error should be different from 54%.

8)The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was \$13,252.  The following year, a random sample of 20 two-year institutions had a mean of \$15,560 and a standard deviation of \$3500.  Is there sufficient evidence at the 1% significance level to conclude that the mean cost has increased?

9)A health researcher read that a 200-pound male can burn an average of 546 calories per hour playing tennis, with a population standard deviation of 3 calories.  Thirty-six males were randomly selected and tested.  The mean number of calories burned per hour was 544.8.  Using the 2% significance level, test the claim that the average