Download Ch 8 Review Stuff

Formulas:
 Bayes’
𝑃 𝐴𝑗 𝐸 =
𝑃(𝐴𝑗 )∙𝑃(𝐸|𝐴𝑗 )
𝑃(𝐸)
when
 𝐏(𝐄) = 𝐏(𝑨𝟏 ) ∙ 𝑷 𝑬 𝑨𝟏 + 𝐏(𝑨𝟐 ) ∙ 𝑷 𝑬 𝑨𝟐 + ⋯ + 𝐏(𝑨𝒏 ) ∙
𝑷 𝑬 𝑨𝒏
𝒏
𝒌
𝒑𝒌 ∙ 𝒒𝒏−𝒌
 Bernoulli
b(n,k;p)=
 Expected Value
𝐸 = 𝑚1 ∙ 𝑝1 + 𝑚2 ∙ 𝑝2 … … . . +𝑚𝑛 ∙ 𝑝𝑛
 W-up : for #1-4 Use the tree to answer the
following questions
purple
K
white
3
4
purple
L
5
11
1.
2.
3.
4.
P(W|K)
P(Y|L)
P(white)
P(K|W)
5. Find the
probability of
throwing a sum of
10 in at least 3
times in 5 throws of
a pair of dice?
white
yellow
6. Three Machines A1, A2, A3, produce 55%, 30%, and 15% of
total production. They produce 1%, 2%, and 3% defective
output respectively. An item chosen at random is defective.
What is the probability that it came from A2?
 7. Colleen bets $1 on a 2-digit number. She wins $75 if
she draws her number from the set of all 2 digit
numbers {00,01,02,03…99}; otherwise she loses her $1.
 A) is this game fair to the player?
 B) how much is Colleen expected to lose in a game?
W-up: ch 9
1. Use calculator to find mean,
population and sample standard
deviation
Class
Frequency
7-10
5
11-14
11
15-18
2
19-22
7
SHOW STEPS – WORK!!
For 2 -4 Given the sample data,
5, 9, 10, 11, 14 find
2. Mean
3. Standard deviation
4. Z-score for 9
5.
Find the area between - .75 and
1.65 standard deviation
6.
Find the area that exceeds 1.85
standard deviations
 7. the weight of 100 college students closely follows a
normal distribution with a mean of 130 pounds and a
standard deviation of 5.2 pounds.
 A) draw a normal bell curve to 3 standard deviations
 B) how many students would you expect to weigh at
least 142 pounds?
 C) what range of weights would you expect to include
the middle 70% of students in this group?
1. 4/7
2. 3/11
3. .4837 4. .2953
Answer to 5
5 1 3 11 2
5 1 5 11 0
5 1 4 11 1
( )( ) ( ) + ( )( ) ( ) + ( )( ) ( ) =
3 12 12
5 12 12
4 12 12
.005
 6. Answer: 𝑃 𝐴2 𝐷 =
=
.006
.016
.3 (.02)
.55 .01 +.3 .02 +.15(.03)
= .375
 7. NO the game is not fair
 She expects to loose 25cents per ticket on average in
the long run
Ch 9 answers
1. 14.26 4.48 4.39
2. 9.8
3. 3.27 (want sample standard deviation)
4. -0.245
5. 0.7239
6. .0322
7. is # 17 on 9.6
Ch 8: Rev: 1-35 Odds are fair game!!
9.5 – standard deviation by hand 1-5
Standard deviation for grouped data using calculator 15
9.6 normal distribution
z-scores, how to read chart, one story prob 11-14,17