Problem 1 (11 Points) complete solutions correct answers key

Problem 1 (11 Points) complete solutions correct answers key

Please match the correct term with each definition below. Please note, you may not use every word in the word bank.

A. Interquartile Range             B. Mean           C. Population   D. Statistic       E. Qualitative Data

F. Standard deviation              G. Range        H. Sample       I. Mode            J. Parameter

K. Quantitative Data                L. Median        M. Census      N. Nominal      O. Ratio

- - The exact center of a data set.

- - A measurement that describes some characteristic of a population.

- - The difference between the 3rd and 1st quartiles.

- - Data that consists of measurements or counts describing numerical information.

- - The average of a data set.

- - The difference between the highest and lowest values in a data set.

- - A subset of a group of objects meant to represent the complete population..

- - The average distance from a point in the data set back to the mean of the data set.

- - Data that can broken up according to some categorical characteristic.

- - The complete collection of all scores, measurements or observations from a group of objects.

- - A measurement that describes some characteristic of a sample.

Problem 2 (14 points)

Shown below is a histogram representing the income of the employees of a local fortune 500 company.

Variable        N   Mean Median   TrMean     StDev

Annual Salary      1000 101165 86734   88756       104296   

Variable              Minimum     Maximum Q1      Q3

Annual Salary        55          812679 29194       141138

A representative of this company then released the following statement:

     “It is a great day for our company when we can finally say that more than half of our workforce is making over $100,000.00 per year. When the average salary is this high we can without reservation claim to be the greatest company to work for in this great nation.”

(a) Do you believe this statement to be an accurate representation of the statistics shown above? Explain your conclusions.

(b) How could you change this statement to accurately portray this information?

Problem 3 (15 Points)

Many of you ride the Appalcart to campus (Boone’s mode of public transportation). For those of you that do ride the bus, you must have also noticed that it is frequently not where it should be when it should be there. The representations below are representative of a random selection of the number of minutes that a given Appalcart bus is behind schedule.

Total

Variable      Count Mean StDev Minimum        Q1     Median       Q3

Appalcart Tardiness   90    9.189 8.309            0.000     2.750     7.250    12.500

Variable             Maximum       IQR

Appalcart Tardiness        36.000       10.250

Descriptive Statistics

      (a) What is the time that breaks this data set into an upper half and a lower half? _______

(b) What is the time that separates the data set into the top 75% and the lower 25%? _______

(c) How many total observations were included in my sample? ______

(d) What is the general shape of the distribution? Explain what statistics you used to determine the shape.

(e) Does this data set display any outliers? If so, estimate the value of the outlier(s).

Problem 4 (12 Points)

One of the major problems facing polling firms today is non-response. Shown below is a table indicating whether or not someone responded to a telephone survey displayed by the age of the individual. Use this table to answer the following questions.

Responded │Age

18-29

30-49

50-69

70 and up

Total

Responded

48

82

95

100

325

Refused

109

69

58

23

259

Total

157

151

153

123

584

(a) What is the probability that a randomly selected individual is 18-29 or refused?

(b) What is the probability that a randomly selected individual is 30-49 or responded?

(c) What is the probability that a randomly selected individual is over 70 and refused?

(d) What is the probability that a randomly selected individual is 50-69 given that they responded?

Problem 5 (15 Points)

A local High School has a Math Club with 20 members ranging in ages from 13 to 18.

(a) How many ways can the offices of president, vice-president, and secretary be filled?

(b) Three senators need to be elected for representation to the local student government. How many different ways can we select three senators?

(c) Students are asked to line up for a photo shoot with all 25 students in a row. What is the probability that they place themselves in alphabetical order?

Problem 6 (21 Points)

Use the probability distribution to answer the following questions.

X

2

3

4

5

6

P(x)

.1

.15

.2

.25

.3

(a) P(x = 6)

(b) P(x = 3)

(c) P(x >3)

(d) P(x> 3)

(e) P(x is at least 4)

(f) P(x is at most 4)

(g) Find the expected value of the probability distribution shown above.

Problem 7 (12 Points)

Use the binomial probability distribution to answer the following questions.

Researchers conducted a study to determine whether there were significant differences in graduation rates between medical students admitted through special programs (such as affirmative action) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 74% for the medical students admitted through special programs.

(a) If 17 of the students from the special programs are randomly selected, find the probability that exactly 10 of them graduated.

(b) If 17 of the students from the special programs are randomly selected, find the probability that fewer than 11 of them graduated.

(c) If 17 of the students from the special programs are randomly selected, find the probability that more than 8 of them graduated.