Misc. Seven Stats Problems

1. A survey of the number of calls received by a sample of Southern Phone Company subscribers last week revealed the following information.

52 43 30 38 30 42 12 46 39 37 34 46 32 18 41 5

a) Develop a stem-and-leaf chart. Above for tips on presenting Stem-Leaf plot.

b) What basic conclusions can be drawn from this chart?

c) Compute the 5 number System for this data set and list Xmin,Q1,Q2,Q3 & Xmax. See Videos and show how the pointer was computed for each quartile.

(15%)

2. For the following table, what is the value of :

a) P(A1)

b) P(B1?A2)

c) P(B2 and A3). Compute this as P(B2)*P(A3? B2) . Rows are B1 & B2: columns are A1, A2 & A3.

What are the values of P(B2) , P(A3|B2) and P(B2&A3)?

In what row and column will you find this answer?

Second Event

First Event

A1 A2 A3 Total

B1 2 1 3 6

B2 1 2 1 4

Total 3 3 4 10

(15 pnts.)

3. The chart below gives the percentage of counties in the US that use various methods for recording votes in 1980 & 2002. Set up side-by-side bar charts by year using the instruction for Side-By-Side Charts in the Class Notes Conference. Copy/Paste your Chart into the TFE Editor from EXCEL.

METHOD 1980 2002

Punch cards 18.5 15.5

Lever machines 36.7 10.6

Paper ballots 40.7 10.5

Optical scan 0.8 43.0

Electronic 0.2 16.3

Mixed 3.1 4.1

(15 pnts.)

4. The following are a sample of the weights of nine jars of peanut butter.

7.69 7.72 7.80 7.86 7.90 7.94 7.97 8.06 8.09

a) Compute the median weight.

b) Compute the standard deviation of the sample using the shortcut formula. Show the formula and values for each term and compute the answer. Use the TFE Equation Editor.

c) Compute the 5 Number System for this data. Just list the values as Xmin=xxx, Q1=xxx,Q2=xxxx,Q3=xxxxx, Xmax = xxxx.

d) Are there outliers? An outlier value is defined as unusually large or small according to the expressions: Answer yes or no.

Outlier > Q3 + 1.5(Q3-Q1) or,

Outlier < Q1-1.5(Q3-Q1)

(15 pnts.)

5. Answer questions a. through f. of 3.23 below.

Show work for part f. only.

(15 pnts.)

6. Compute the mean and standard deviation for the data in the table below. State your assumptions and show all calculations. See Video- Mean & Variance for Grouped Data in Videos –Topics In Stat 230(1) conference.

Distance Frequency

0 to 5

5 to 10

10 to 15

15 to 20

20 to 25 4

15

27

18

6

(10%)

7. A box contains 3 red balls and 4 green balls. If two balls are randomly selected in sequence, what is the possibility that a red ball and a green ball are picked out of the box. State the rule for P(A&B) and then substitute the values and compute the answer.