LSP 121

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 216 from hex to decimal [SHOW WORK]

3 8 F 2

Put powers of 16 (right to left) above the cells.160 = 1, 161 = 16, 163 = 256, 164 = 4096

Multiply lower number times upper number. Remember A = 10, B = 11, C = 12, … F = 15 Add these four products.

Converting base 16 to decimal

4096 256 16 1

0 0

1 1

2 2

3 3

4 4

5 5

6 6

7 7

8 8

9 9

10 A

11 B

12 C

13 D

14 E

15 F

DEC HEX DEC HEX DEC HEX DEC HEX

• There is 1/36 chance of rolling two sixes

• P(not A) = 1 – P(A)

• 1 – 1/36 = 35/36 or .972

4) What is the probability of NOT rolling a double-6 with two dice?

• odds are calculated by usingP(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

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

• 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

6) What is the probability of the next 5 births at a hospital all being girls?

• 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 ]

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?

• For CA227,381 deaths / 30,000,000 ppl = 0.00758multiply this by 1000 = 7.58 deaths / 1000

• For AK2,911 deaths / 550,000 ppl = 0.005293multiply this by 1000 = 5.29 deaths / 1000

• Don’t forget to answer the questions included with this problem

8) see problem

9a) How many different license plates are possible if you have plates with 3 letters followed by 3 numerals?

26 26 26 10 10 10

Use 6 boxes and enter the possible number of values for each part of the license plate:

Multiply these numbers and you get:

17,576,000 possible plates

• Use 10 boxes and the possible notes per box:

9b) How many different 10-note “tunes” can be created from the notes A, B, C, D, E, F and G?

7 7 7 7 7 7 7 7 7 7

Multiply or calculate 710 and you get

282,475,249 possible “tunes”

problem 10

• 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

Problems 11, 12

• 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’

• 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

11) use Excel to work this out, see below

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)

indicates base 2

• 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

12) use Excel to work this out, similar to 11), see below

Bandwidth Data rate in Hertz

1000 =2*A1*log(8,2)

1500 =2*A2*log(8,2)

2000 =2*A3*log(8,2)

13. Programming question

• keep track of the value of i and j and work through the nested loops

• total number of outputs: 40

• start with this

i j OUTPUT.SCREEN i,j

1 1 1 1

1 2 1 2

1 3 1 3

2 1 2 1

2 2 2 2 … etc

another method..

• You can enter the following as ‘code’ in VBA for Excel

FOR i = 1 TO 4FOR j = 1 TO 3 MsgBox i & “ “ & jNext jNext i

• Then ‘Run’ the macro in Excel• Notice there will be 4 x 3 outputs (12)

Standard HTML

• <html>

• <head><title> … </title></head>

• <body>

• .. contents of body

• </body>

• </html>

• DO NOT REPEAT html, head, or body

Insert javascript in webpage

• 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

Macros and VBA

• 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)

What is an algorithm, #16

• 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

Q 17, risk analysis

• 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:

Tumor is cancerous

Tumor is benign Totals

Positive 75% of 1.67 = 1.25true positives

Negativefalse negatives

75% of 9998.33 = 7498.75

Total 1/6000 * 10000 = 1.67

9998.33 10,000

Find the 4 missing values (the true positives and true negatives have been filled in).

Now find

• 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)