1. AP STAT MOCK EXAM Saturday, April 23, 2016

2. EQ: How do you solve probability questions in a binomial setting?
Advanced Placement Statistics Section 8.1: Binomial Distributions (Part I)
EQ: How do you solve probability questions in a binomial setting?

3. DOES NOT IMPLY 50%/50% PROBABLITY OF OUTCOMES
Terms to Recall/Know: X
discrete number
0 to n
Random Variable
Binary – 2 possible outcomes
Examples:
ON or OFF
MALE or FEMALE
HIT or MISS
DOES NOT IMPLY 50%/50% PROBABLITY OF OUTCOMES

4. B(n, p) Binomial Random Variable X # of successful outcomes
Binomial Probability Distribution n
# of total outcomes
probability of success for any
1 observation p q
probability of failure for any
1 observation

5. Four Properties of a Binomial Experiment:
parameter
population
Four Properties of a Binomial Experiment:
1. fixed number of trials
n = # of [in context]
2. each trial results in a success or failure (disjoint)
S= [define success]
F= [define failure]

6. 3. outcomes of trials are independent
probability of each success is the same
from trial to trial
Recall: Complements
If S is success, and F is failure, then P(F) = 1 – P(S).

7. Does this meet the 4 properties of a binomial distribution?
Read Ex 8.1, p. 514
Does this meet the 4 properties of a binomial distribution?
1) Fixed number of trials?
n= 5 children
2) Success/Failure?
S = having type O blood
F = not having type O blood
3) Independence?
Blood type is independent from one person to another
4) Probability of success the same?
p = 0.25 and q = 0.75

8. Read Ex 8.2, p. 514 3) Independence?
Does this meet the 4 properties of a binomial distribution?
1) Fixed number of trials?
2) Success/Failure?
3) Independence?
NO, IT’S WITHOUT REPLACEMENT!!
4) Probability of success the same?
Therefore this distribution cannot be written
B(n, p)

9. In class Assignment: p. 516 #1 - 6#2 #3 #4 #5 #6
NO; n not a fixed value
YES; define all properties in context
YES; define all properties in context
NO; n not a fixed value
NO; probability of success likely not to remain the same
YES; define all properties in context

10. Handout WS Examples Section 8.1 Complete Ex 1
Ex.1 The Heart Association claims that only 10% of American adults over 30 can pass the President’s Physical Fitness Commission minimum requirements. Suppose 4 adults are randomly selected and each is given the fitness test.
What is the observation of interest?
b) Justify in context of the problem that this setting meets the properties of a binomial distribution.
The observation of interest is the result of the fitness test.
fixed number of trials; n = 4 adults
success = adult passes test, failure = adult fails the test
Each adult’s test result is independent of another adult’s test result.
Probability of success and failure remains the same from trial to trial. P(passes test) = P(fails test) = 0.9

11. SSSS (.1)(.1)(.1)(.1) = 0.0001 Intersection FFFF
FSSS
SFSS
SSFS
SSSF
FFSS
FSFS
FSSF
SFFS
SFSF
SSFF
SFFF
FSFF
FFSF
FFFS
FFFF
SSSS
(.1)(.1)(.1)(.1) =
Intersection
FFFF
(.9)(.9)(.9)(.9) =
SSSF
(.1)(.1)(.1)(.9)(4) = .0036
SSFF
(.1)(.1)(.9)(.9)(6) = .0486
SFFF
(.1)(.9)(.9)(.9)(4) = .2916 X 1 2 3 4
P(X)
.6561
.2916
.0486
.0036
.0001
= 1

12. RECALL: Formulas to Know:
“n factorial”
n(n - 1)(n – 2)…(1)
Ex ! = (5)(4)(3)(2)(1) = 120
Combinations
also called the “binomial coefficient”

13. X = number of adults who pass a fitness test out of 4
Binomial Probability
Go back to WS Ex 1. Find f) and g):
X = number of adults who pass a fitness test out of 4
randomly selected adults taking the test
f) P(X = 3) =
g) P(X = 2) =

15. RECALL: CALCULATOR FUNCTIONS:
binomialpdf (n, p, x)
For one specific value
Ex. Find the probability of 5 successes in 8 trials where the probability of success is 40%.
P(X = 5) = ___________
0.1239
binomialpdf (8, 0.4, 5)

16. Cumulative Probability Density Function
binomialcdf (n, p, x)
For cumulative values
Ex. Find the probability of less than 5 successes in 8 trials where the probability of success is 40%.
P(X < 5) = _____ means P(X < 4) = ____
0.8263
0.8263
P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = _____
binomialcdf (8, 0.4, 4)

17. Ex. Find the probability of at least 5 successes in 8 trials where the probability of success is 40%.
0.1736
1 - binomialcdf (8, 0.4, 4)
Ex. Find the probability of more than 5 successes in 8 trials where the probability of success is 40%.
0.0498
1 - binomialcdf (8, 0.4, 5)

18. Go back to Handout WS Examples Section 8.1 Complete Ex 2
Ex. 2 Periodically the FTC monitors the pricing accuracy of electric checkout
scanners at stores to ensure consumers are charged the correct price at checkouts. A 2004 study of over 100,000 items found that one of every 30 items is priced incorrectly by scanners. Suppose the FTC randomly selected five items at a retail store and checks the accuracy of the scanner price of each.
a) Determine if this experiment meets the criteria of a binomial experiment.
fixed number of trials; n = 5 items scanned
success = item accurately scanned, failure = item inaccurately scanned
Result of one item scanned is independent of the result of another item scanned.
Probability of success and failure remains the same from trial to trial. P(item accurately scanned) = 29/ P(item inaccurately scanned) = 1/30

19. Define the random variable X then create a probability distribution table.
X =
Create a cumulative probability distribution table.
number of items accurately scanned out of 5 items scanned at a retail store X 1 2 3 4 5
P(X)
4.12x10-8
5.97x10-6
. 0003
. 1455
. 8441
RECALL: X 1 2 3 4 5
F(X)
4.12x10-8
6.01x10-6
3.52x10-4
.0104
.1559 1

20. d) What is the probability that at most 2 items are priced incorrectly?
P(________) =
e) What is the probability that at least one of the 5 items is priced incorrectly?
P( _________) =
X > 3
.9997
means at least 3 are priced correctly
X < 4
means at most 4 are priced correctly
1 – P(X = 5)= 1 – =

21. XL1 binomialpdf(5, 29/30, L1) L2
Define the random variable X then create a probability distribution table.
X =
Create a cumulative probability distribution table.
number of items accurately scanned out of 5 items scanned at a retail store
How can you use lists to calculate these values?
XL binomialpdf(5, 29/30, L1) L2
cumsum (L2)L or sum (L2)L3

22. ASSIGNMENT:
p #