final exam review

1) The Pacific tectonic plate moves at a rate of 4”/year. What is this in miles per hour?
•
• 4 in x yr x da x ft x mi yr 365 da 24 hr 12 in 5280 ft
4 miles
365 x 24 x 12 x 5280 hr
• = 7.2 x 10 -9 mi/hr

2) Convert 1 0 1 1 0 1 0 0
2 from binary to decimal [SHOW WORK]
1 0 1 1 0 1 0 0
Write powers of 2, right to left, then sum the numbers above the 1’s
128 64 32 16 8 4 2 1
1 0 1 1 0 1 0 0
128 + 32 + 16 + 4 = 180 (ans)

3) Convert 3 8 F 2
16 from hex to decimal [SHOW WORK]
3 8 F
Put powers of 16 (right to left) above the cells.
16 0 = 1, 16 1 = 16, 16 3 = 256, 16 4 = 4096
Multiply lower number times upper number.
Remember A = 10, B = 11, C = 12, … F = 15
Add these four products.
2

4096 256 16 1
DEC HEX
0 0
1 1
2 2
3 3
DEC HEX
4 4
5 5
6 6
7 7
DEC HEX
8 8
9 9
10 A
11 B
DEC HEX
12 C
13 D
14 E
15 F

4) What is the probability of NOT rolling a double-6 with two dice?
• There is 1/36 chance of rolling two sixes
• P(not A) = 1 – P(A)
• 1 – 1/36 = 35/36 or .972

5) Suppose event A has a 0.98 probability of occurring and event B has a 0.94 probability of occurring. Compute the
ODDS for event A and the ODDS for event B
• odds are calculated by using
P(A) / P(not A)
• Odds for event A =
0.98 / 0.02 = 49/1 or 49 to 1
• Odds for event B =
0.94 / 0.06 = 15.67/1 or 15.7 to 1

6) What is the probability of the next 5 births at a hospital all being girls?
• Probability of multiple events is calculated by the product of the probabilities
• ½ * ½ * ½ * ½ * ½ = 1/32 or .031
• You can also show: (1/2) 5 = 1/32

7) If Peoria, IL is hit by a tornado about every 30 years, what is the probability that Peoria will be hit by a tornado this year?
• simply 1/30
• What is the probability that Peoria will be hit by tornados in three consecutive years?
• 1/30 * 1/30 * 1/30 = 1/27,000
• at least once in the next 30 years?
• 1 – (not A) 30 = 1 – (29/30) 30 =
• ANS = .64 [ .6383 ]

8) see problem
• For CA
227,381 deaths / 30,000,000 ppl = 0.00758
multiply this by 1000 = 7.58 deaths / 1000
• For AK
2,911 deaths / 550,000 ppl = 0.005293
multiply this by 1000 = 5.29 deaths / 1000
• Don’t forget to answer the questions included with this problem

9a) How many different license plates are possible if you have plates with 3 letters followed by 3 numerals?
Use 6 boxes and enter the possible number of values for each part of the license plate:
26 26 26 10 10
Multiply these numbers and you get:
17,576,000 possible plates
10

9b) How many different 10note “tunes” can be created from the notes A, B, C, D, E, F and G?
• Use 10 boxes and the possible notes per box:
7 7 7 7 7 7 7 7 7 7
Multiply or calculate 7 10 and you get
282,475,249 possible “tunes”

• Lottery ticket costs $2, so you start with
2 * 1, then add the possible ‘wins’
• 2*1/50 + 1,000*1/2,000 + 2,000*1/4,000 +
20,000*1/40,000 …
• -$2 + .04 + .50 + .50 + .50
• expected value = - 0.96
• you lose

• If you get a problem like 10 or 11 on the exam you will be given the Excel formula required to do the calculations
• remember, in Excel
=log(x,b) means the log of ‘x’, base ‘b’

11) use Excel to work this out, see below
• Note signal = .4 and noise = .0002
• in Excel set up 2 columns
• 1000 to 10,000 increments of 500, and
• = cell * log ((1 + .4/.0002), 2 ), looks like
• with 1000 in cell A1, 1500 in cell A2 indicates base 2
Frequency (Hz) Bits per second
1000 =A1*log((1+.4/.0002),2)
1500 =A2*log((1+.4/.0002),2)
2000 =A2*log((1+.4/.0002),2)

12) use Excel to work this out, similar to 11), see below
• Note W =frequency and M = 8
• in Excel set up 2 columns
• 1000 to 10,000 increments of 500, and
• = 2 * cell * log (8, 2 ), looks like
• with 1000 in cell A1, 1500 in cell A2
Bandwidth Data rate in Hertz
1000 =2*A1*log(8,2)
1500 =2*A2*log(8,2)
2000 =2*A3*log(8,2)

• keep track of the value of i and j and work through the nested loops
• total number of outputs: 40
• start with this
1
1 i
1
2
2
2
3 j
1
1
2
OUTPUT.SCREEN i,j
1 1
1 2
1 3
2 1
2
2 … etc

• You can enter the following as ‘code’ in
VBA for Excel
FOR i = 1 TO 4
FOR j = 1 TO 3
MsgBox i & “ “ & j
Next j
Next i
• Then ‘Run’ the macro in Excel
• Notice there will be 4 x 3 outputs (12)

• <html>
• <head><title> … </title></head>
• <body>
• .. contents of body
• </body>
• </html>
• DO NOT REPEAT html, head, or body

• The following is a ‘trigger’ in HTML code that signals some javascript (what is in italics is explanatory and not actual code
• <script type = “text/javascript”>
• … java script code follows
• </script> is used to end the javascript part

• relates to question 14, 15
• macro is best used when
– you have to repeat a complex operation
– a single operation involves many steps
– for simulations
• given: CELLS(2,3) = CELLS(2,3)+4
– this will add 4 to contents of cell row 2, column 3; that sum is put in cell(2,3)

• An orderly sequence of steps that can be followed to produce a desired result
• Algorithms are used in
– manufacturing
– testing
– computer programming languages
– making decisions

• First note what is GIVEN
– expected probability of cancer 1/6000 =
0.017%
– reliability of test = 75%
– number of people with tumors = 10,000
• To find:
– percentage that will receive a true positive
– percentage that will receive a false negative

Use the 5 steps to complete the matrix
• Beginning of matrix:
Positive
Negative
Total
Tumor is cancerous
75% of 1.67 = 1.25
true positives
Tumor is benign false negatives
1/6000 * 10000 =
1.67
75% of 9998.33 =
7498.75
9998.33
Totals
10,000
Find the 4 missing values (the true positives and true negatives have been filled in).

• Percentage of true positives
– 1.25 divided by total positives (express this as a percentage)
• Percentage of false negatives
– false negatives are negative test results which in fact are cancerous (not calculated yet)
– divide this by the total number of negatives
(far right column in negative row)