# MATHEMATICS

The SmartMinds University collects a variety of statistics about its students.  The database includes the following data:

(a) Student’s academic class {Freshman, Sophomore, Junior, Senior}
(b) Student’s ethnicity
(c) Student’s age category: {18-20, 21-25, 26-30, over 30}
(d) Student’s preferred classroom temperature (in degrees Fahrenheit)
(e) Student’s height and weight
(f) Number of students in each dorm room
(g) Student’s year of birth
(h) Student’s satisfaction rating on a scale of 1-10
(i) If the student smokes {yes, no}
(j)    Student’s preferred TV channel {Entertainment, History, HBO, CNN, ESPN}

[A (10 points)]
For each of the questions, indicate with an “X” what scale the data is measured on.
Question Nominal Ordinal Interval Ratio
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)

[B (10 points)]
For each of the questions, indicate with an “X” if the measurement is Qualitative, Quantitative Discrete or Quantitative Continuous.
Question Qualitative Quantitative Discrete Quantitative Continuous
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)

[C (12 points)]
GRE Scores: The following are the quantitative GRE scores of the graduate students from one of the Mathematics department:
777 765 758 788 766 750 759 755 788
749 758 742 780 740 765 787 766 766

a. Construct a grouped frequency distribution with 5 classes.

b. Use Excel to construct a Histogram.  (Tools  Data Analysis  Histogram  for input range select the given values, for the bin range select the classes upper boundaries values  check Chart Output)

Note: give a brief explanation by specifying the covered steps.
Highest
Lowest
Range
Class width

Grouped frequency distribution
Class limits Class boundaries Frequency

[D (13 POINTS)]
For the set of data given above (on point C), calculate the following descriptive statistics (Briefly explain the median, mode, and quartiles. For quartiles calculations, follow the way is explained in the homework2).  You can use any excel tools as long as you show your work.

Mean
Median
Mode
1ST Quartile
3rd Quartile
Interquartile Range
Range
Standard Deviation
Variance

b.   Compute the z-scores.  Give the formula you used.

[E (10 points)]
SmartMinds University is running a promotional raffle that offers a chance to win either a 1-year discount on tuition cost (which results in a \$500 savings) or a 2-year discount on bookstore purchases (which results in a \$300 savings).
• Winning a tuition discount has a 1-in-500 chance.
• Winning a bookstore purchases discount has a 1-in-20 chance.

Is this promotion worth it if the tickets cost \$20?

B. Determine the appropriate statistical term:
Selecting 64 customers to study without regard to their data is called creating a(n) _________.
The data for all customers is called a(n) _______.

[F1 (15 points)]  ONLY if you cannot answer F1, for partial credit (8 points) answer F2.
Some additional collected data is presented in the table below:

Age Category

College {18-20} {21 – 25} {26-30} Above 30
Kings 500 100 400 100
Falcon 300 250 100 200
Priestley 900 700 800 600
Give the literal formula first (not with numbers) and then solve:
“What is the probability of being in the lowest age category given that you are a student of Priestley College?”
Give the literal  formula first (not with numbers) and then solve:
“What is the probability of being either a Kings College or a Falcon College student?”
Give the literal formula first (not with numbers) and then solve: “What is the probability of being younger than 26 years given that you are a student of Priestley College?”
Give the literal  formula first (not with numbers) and then solve:
“What is the probability of not being a student of Kings College?”
Is there any relationship between being a member older than 30 and belonging to a specific College? (relationship between age and College)

[F2 (8 points)]
Another survey examined the student’s preferences in having lunch available on campus.
Have Lunch (L) Not have Lunch (L’)
Male Student (M) 2500 3000
Female Student (F) 1700 1000
a) Compute the Marginal Probabilities and the Joint Probabilities.

Marginal Probability Joint Probability

b) Compute: P(L|M), P(M or L)

[G (30 points)]
Overall, the students’ class attendance days (per year academic) is normally distributed around 180 days with a standard deviation of 20 days.

What’s the probability that the mean number of attendance days will be between 190 and 200?
Students that are in the top 10% will receive a 20% off coupon at the “Crazy” cafeteria.  What is the minimum number of attendance days that you should have in order to receive such discount?
The students at or below the 15%ile of number of attendance days must attend a counseling session with one of the advisers. At least how many attendance days you should have in order to not have to attend such session?
How likely (what is the probability) is it that Cri (name not previously mentioned) will have her attendance days between 170 and 195 days?
What percentile does an attendance of 200 attendance days rank at?
What percentile does an attendance of 180 attendance days rank at?
How likely (what is the probability) is it to have the number of days attended below 170?
If 36 students (36 = size of the sample) selected randomly attended the school, what’s the likelihood that their mean number of attended days will be within 2 days of the population mean? (mean +/- 2)

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