1. Fill in the Table below characterizing the following data sets

(a)Vehicle miles per gallon (mpg):15.6, 21.78, 30.0, 53.1, 11.5

(b) Coins in a piggy bank: 47 pennies, 30 nickels, 25 dimes, 15 quarters

(c) Colors of cars driving daily in front of your house: 10 red, 14 tan, 27 white, 18 black

(d) Number of students in the 4 grades of high school: 220 F, 260 S, 275 J,310 Seniors

(e) Number of students in 5 High Schools in your town: 1500, 2100, 1400, 4020, 1200

(f) Amount spent (5 families) on groceries annually: $10359, $12480, $6500, $18237, $11,238

(g) Change in the pockets of 5 persons: $2.37, $1.11, $1.97,$3.05, $25.00

(h) Ratings of a new android phone: 5,000 5-star, 10,000 4-star, 1,300 3-star,500 2-star, 1500 1-star

(i) A student's grade point average (4=A, 3=B, 2=C, 1=D, 0=F) 15 A's, 13 B's,10 C's, 2-D's, 1-F

( )	QUALITATIVE / QUANTITATIVE	DISCRETE / CONTINUOUS	SCALE	VALID STATISTICS POSSIBLE mean, mode, etc. NOT calculations	Most appropriate measure of CENTER & DISPERSION
a
b
c
d
e
f
g
h
i

2. Describe which SAMPLING method is being used in the examples below and explain your choice:

(a) We want to know the number of certified mechanics employed by 30 dealerships in a city. We randomly select (e.g., names out of a hat) 7 of these dealerships and survey every mechanic employed there.

(b)Let's say UMGC has 15 Departments and we want to know the average number of hours students whose major is in that Department spend on coursework. We randomly sample (each student assigned a number and random number generated selection)20 students from each department.

(c)You train 300 recruits a cycle on rifle practice and they get a score. The average score is not that meaningful for your purpose, so you decide to check the scores of 20% of these recruits (60 recruits). The unalphabetized names are on a list and you select every 5^th name until you get your 60.

(d)There is a "block party" and you ask everyone there what their income is.

3. Are any of the following sampling methods BIASED? If so, why or how? Could any still be valid? Why?

(a)Cell phone survey (b) Landline phone survey (c) Mailed out/mail-back survey (d) Door-to-door survey (f) Asking persons in your neighborhood their movie preference (g) Emailed survey (h) Asking a "person on the street" survey

4. You bought a bag of M&M's which has 15 reds, 13 greens, 16 yellows, and 10 browns in it WELL MIXED. You prefer the red ones.

(a)What is the probability if you reach in blindly and pull one out, that it is red?

(b)You pulled out a green one but ate it anyway.You reach in again, blindly, what is the probability you get a red one this second try?

5. Here are 30 data values (data points): 45, 1, 16, 36, 5, 34, 15, 99, 68, 23, 12, 7, 3, 12, 5, 5, 43, 40, 55, 52, 28, 70, 2, 25, 19, 41, 22, 28, 20, 40 (When entering these into Excel MAKE SURE you have all 30 data values covered)

(a)Construct a SCATTER PLOT of the RAW data (NOT rank-ordered)

(b) Calculate the mean, median, mode, variance, standard deviation, Q1, Q2, Q3, IQR, and the data value that is the 80^th percentile (calculate its rand and then what that data value is in the rank-ordered data set).

(c) Construct a FREQUENCY TABLE using ranges 1-10, 11-20, 21-30, etc. until all data would be included. Include the Frequencies, Relative Frequencies, and Cumulative Relative Frequencies as decimal fractions (e.g., 0.234 keeping only 2 or 3 decimal places)

(d)Find any UNUSUAL data points using BOTH the Mean +/- 2* SD and the Mean +/- 1.5 * IQR

(e)Construct a BAR CHART using the RELATIVEFREQUENCIES and construct a HISTOGRAM using the FREQUENCIES.

(f)If all 30 numbers on separate pieces of paper were put in a hat and one was blindly drawn out, what is the probability it is a number less than 40?, Greater than 50? Between 31 and 60?

6. You have a deck of regular playing cards (4 suits, 13 cards in each suit, and values are ace to 10 and jack, queen king face cards). You shuffle them thoroughly and turn the top five over.

(a) What is the probability you have a Royal Flush ( Ace, King, Queen, Jack, Ten) all of the Hearts?

(b)What is the probability you have 3 Aces, and 2 eights? (bad luck for one thing).

7. You take your dog to the Vet for its annual rabies shot. Sitting in the waiting room are a number of other animals. 65% of those need their distemper shots and 17% have the "mange", and 5% need the shot and have mange.

(a) What is the probability the next animal called in (forget appointments) will have mange OR need the distemper shot?

8. You manage a sales office and have 25 salespersons at the morning meeting. Nine clients need attention. Assume all the salespersons can handle the assignment

(a)How many ways can you assign the 25 salespersons to the 9 clients?

9. Here are 7 letters W, F, G, H, P, X, V

(a)How many COMBINATIONS can you make using ALL 7 letters?How many PERMUTATIONS?

(b)How many COMBINATIONS can you make using only 4 of the 7 letters? How many PERMUTATIONS?

(c) pt BONUS: How many PERMUTATIONS can you make from all 8 of these letters: I L L I N O I S

10. Solve these equations for these numbers: 4, 6, 3, 5

(a) ( X²) = ______ (b) ( X) ²= ______

11. (2 pts)You sample 10,000 persons to find out how many vehicles they own and use the sample probabilities to (estimate) thePopulation mean (), variance (² ), and standard deviation ()

x	P(x)	x * P(x)	(x -)	(x -)2	(x -)2 * P(x)
0	0.05
1	0.25
2	0.40
3	0.15
4	0.10
5	0.05
TOTALS	1.00	(MEAN):			VARIANCE:

STD DEVIATION:

12. (2 pts) BINOMIAL PROBLEM: CALCULATE PROBABILITIES OF THE x-VALUES = P(x) Given that n = 4 and p = .75

(a) Complete the Table using the formula you used for "Rainy Days" AND Excel's BINOM.DISTfunction for software.

x	P(x) (Formula)	P(x) Software
0
1
2
3
4
SUM

(b) NORMAL APPROXIMATION of the Binomial: MEAN = n * p = ____ Variance = npq = ____ SD = sqrt(npq)=____

13. (2 pts) Here is a five number data set: 21, 35, 46, 57, 62

(a) Calculate the mean ____ and std deviation______.

(b) Complete the Table (get probabilities from the z-Tables):

x-values	21	35	46	57	62
z-values
Probability of this value or LOWER
Probability of this value or GREATER