MAT 308 Assignment Problems 2015 | Complete Solution

In this assignment you may use your book, your notes and your calculator.  SHOW YOUR WORK WHERE STATED TO DO SO TO RECEIVE FULL CREDIT.  Round all decimal answers to 4 decimal places.

1. The population of the City of Baltimore is 622,104 (as of July 1, 2013).  Mayor Rawlings-Blake would like a survey of the residents of Baltimore to determine if they are satisfied with how Monday’s riots were handled.  How could a survey be developed that is unbiased and addresses a representative sample of the population? 

2. What is the difference between qualitative and quantitative data?  Give an example of each.

Consider the data below for questions 3--4.

3.            What number best represents the 25th percentile?

4.            Prove or disprove the existence of outliers.

6. Determine the mean, median and mode for the data below.    Which measure of central tendency best represents the data?  Provide reasoning supporting your answer.

Number of Days Absent per Student, Mr. Steven’s 6^th grade class

7                      5              12           3              0              5              13           12           5              0              6              38

11.                 0              1              4              9              11           2              3              6              0              1              1

7. Jason and Mary took an entrance exam with a certain company.  Jason scored a 76%.  His cohort’s average was 80% with a standard deviation of 5%.  Mary also scored a 76%.  Her cohort’s average was an 83% with a standard deviation of 8%.   Determine a z-score for each person and compare their scores using z-scores.  SHOW YOUR WORK

8. A gumball machine contains 10 blue, 5 pink, 5 orange, 16 yellow and 14 white gumballs.  What is the probability that a child receives a yellow followed by a white?  (No replacement)     SHOW YOUR WORK

9. Find the probability of rolling two dice and getting a sum of eight.  SHOW/EXPLAIN YOUR WORK

10. 60 high school seniors are athletes.  Of the seniors, 15 play soccer, 10 run cross country and 2 play soccer and run cross county.  If one senior is selected at random for an athletic scholarship, what is the probability that the student is either a soccer player or a cross country runner? SHOW/EXPLAIN YOUR WORK

11. In how many ways can 3 employees be selected to serve on a task force, if there are 12 employees?

12.  One card is selected from a standard deck of cards.  What is the probability that it is a heart, given that it is a queen?

13. Suppose that the probability of your favorite baseball player getting a hit at bat is 0.45.  Assume that each at bat is independent.  What is the probability that he bats eight times and gets exactly four hits?    SHOW/EXPLAIN YOUR WORK

14. On a given weekend, sobriety checkpoints average 10 DUI drivers.  What is the probability that sobriety checkpoints will catch 20 or fewer DUI driver in a given month?  (4 weekends)  SHOW/EXPLAIN YOUR WORK

15. Find the specified probability.  Label the associated diagram.     P(z > 1.43)  SHOW/EXPLAIN YOUR WORK

16. According to the Centers for Disease Control and Prevention, the total blood cholesterol levels in Americans are found to be normally distributed with a mean of 200 mg/dl and a standard deviation of 18 mg/dl.  Determine the percentage of the population who have blood cholesterol levels between 182 and 218 mg/dl and label the associated diagram.  SHOW/EXPLAIN YOUR WORK

17. Suppose that the weights of female college students are normally distributed with a mean of 150 pounds and a standard deviation of 20 pounds.  What weight represents the third quartile for female college students?  SHOW/EXPLAIN YOUR WORK

18. The confidence interval for a population mean is 17.8 < μ < 22.4.  What is the margin of error? SHOW/EXPLAIN YOUR WORK

Consider the following information for questions 19-21.  Construct a 95% confidence interval for the mean.

The president of a small community college wishes to estimate the average distance commuting student’s travel to the campus.  A SRS of 12 students yielded the following distances in miles:  27,35,33,30,39,25,38,22,27,37,33,40. 

19. State the point estimate.

20. Determine the margin of error for a 95% level of confidence.  SHOW/EXPLAIN YOUR WORK.  INCLUDE FORMULA.

21. Construct a 95% confidence interval for the population mean distance commuting students travel to the campus. 

22. A manufacturer is testing the variance in the outer diameter of couplings.  The diameters are measured in millimeters, and a random sample of 25 couplings has a sample variance of 2 mm.   Construct a 95% confidence interval for the variance.  SHOW YOUR WORK. INCLUDE FORMULA.

Consider the following information for questions 23-25.

Each bottle of fruit juice from a small manufacturing plant is supposed to contain exactly 12 fluid ounces of juice.  Susan is in charge of quality control and decided to test this claim by gathering a SRS of 30 bottles.  She will recalibrate the machinery if the average amount of juice per bottle differs from 12 fluid ounces at the 1% level of significance.  Her sample of 30 bottles has an average of 11.92 fluid ounces and a sample standard deviation of 0.26 fluid ounces.  Conduct a hypothesis test to determine if the machinery needs recalibrated.

23.  State hypotheses:

24.  Calculate test statistic and/or p-value.  SHOW YOUR WORK. INCLUDE FORMULA.

25. Conclude your test.  Justify your answer.  What does your answer imply about the machine?

Consider the following information for questions 26-27.

A restaurant claims that the standard deviation in the length of serving times is less than 2.9 minutes.  A disgruntled customer believes that the standard deviation is more than 2.9 minutes.  He takes a random sample of 23 serving times, which has a standard deviation of 3.5 minutes.  At α = 0.10, is there enough evidence to support the customer’s claim?  Assume the population is normally distributed. 

26. State hypotheses:

27. Calculate test statistic.   SHOW YOUR WORK. INCLUDE FORMULA.

28. Conclude your test.  Justify your answer.  What does your answer imply about the customer?

Consider the data below for questions 29-30.

High School GPA               3.5          2.5          4.0          3.8          2.8          1.9          3.2          3.7          2.7          3.3

First-Year College GPA   3.3          2.2          3.6          3.7          3.3          2.0          3.1          3.4          2.3          3.1

29. Determine the least squares regression line.  State the correlation coefficient and its meaning.

30.  Use your regression line above to predict the GPA of a first-year college student who had a 3.5 GPA in high school.