Transcript final exam hints

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
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.
2
Converting base 16 to decimal
4096
256
DEC
HEX
0
16
1
DEC HEX
DEC HEX
DEC HEX
0
4
4
8
8
12
C
1
1
5
5
9
9
13
D
2
2
6
6
10
A
14
E
3
3
7
7
11
B
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
Multiply these numbers and you get:
17,576,000 possible plates
10
10
10
9b) How many different 10-note “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 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’
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
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
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)
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 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)
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
Positive
Negative
Total
Tumor is benign
Totals
75% of 1.67 = 1.25
true positives
false negatives
1/6000 * 10000 =
1.67
75% of 9998.33 =
7498.75
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)