Warm-up
6.2 Binomial Distribution (Day 2)
Student of the day!
Block 4
Student of the day!
Block 5
Review of binompdf and binomcdf
1) It is estimated that 15% of the population suffers some
form of mental illness at one point of their lives. In a small
company that employs 20 employees. Determine the
probability that 2 employees suffer or had suffered some
form of mental illness.
2) Delores has a free-throw shooting percentage of 0.65.
What is the probability that she makes no more than 5
free throws out of 10 attempts?
6.2 Binomial Distribution Formulas
vs. Probability Distribution Formulas
Probability Distribution
u x   xi pi

2
x

 (x
  x )  pi
2
i
Binomial Distribution
u x  np

2
x
 n p (1  p )
6.2 (Day 2) Binomial Distribution
Finding the mean and SD
Characteristics of Binomial
Distribution: E ( x )   x
x 
n p
np 1  p 
As n increases, the distribution becomes more normal.
Shape, Center and Spread
H.W. and quiz next block
6.2 E #23-25
Be ready for a quiz on 6.1 and 6.2
You will be given the following formulas on the
day of the quiz:
2
2
E(x)   x   x i p i
Var  x    x   ( x i  u x ) p i
For binomial
 x  nk
distributi
 
on
np (1  p )
Conclusions from Student Feedback
A.P. Statistics
Good and should keep
Changes and or/ ideas
• Printed Notes
• More A.P. type questions
• Documents on Sharepoint
- I have incorporated A.P.
• Clearly labeled daily schedule
released Qs.
• Practice Tests
- I will include more A.P. type
• Collaborative Work
questions in a game or activity
• Student of the day!
for each chapter.
FYI: The calculator can be used on • Reduce # of items on agenda
all the exam. There is no non• ½ the class likes activities and
calculator section.
other don’t.
Those of you that want access to
- Solution: differentiated
A.P. Released Material, bring a
instruction, there will be days
flashdrive and come in during
where you can chose to do an
Block 7. I will be happy to give you
activity or A.P. type questions
files.
Multiple Choice Practice on Probability
1) A binomial event has n = 60 trials. The probability
of success on each trial is 0.4. Let X be the count of
the successes of the event during the 60 trials. What
are  x and  x (s.d) ?
(a) 24, 3.79
(b) 24, 14.4
(c) 4.9, 3.79
(d) 4.90, 14.4
(e) 2.4, 3.79
2) Consider repeated trials of a binomial random variable.
Suppose the probability of the first success occurring on
the second trial is 0.25. What is the probability on the
first trial?
(a)¼
(b)1
(c)½
(d)1/8
(e)3/16
3) Russell’s parents buy two apples each weekend, and put
them in his lunch on two randomly selected weekdays of
the following week. What is the probability that Russell
gets an apple on exactly one of Monday or Tuesday next
week.
(a)
  ( 0 .4 )
5
2
2
( 0 .6 )
3
(b) 2
  ( 0 .4 ) ( 0 .6 )
(c) 2
 ( 0 .4 )( 0 .6 )
5
1
5
2
1
4
(d)
4
6
10
(e)  2   2 
2 1
       
5 5 5 4
4) Delores has a free-shooting percentage of 0.65. What is
the probability that the first free throw she manages to
make is on her 4th attempt. Which of the following
would lead to the correct answer?
(a) Binomcdf (4, 0.65, 1)
(b) Binompdf(4, 0.65, 1)
(c) (0.65)(1-0.65)3
(d) 4 ( 0 . 65 )(1  0 . 65 ) 3

1
BONUS QUESTION!
At Kennett High School, 5% of athletes play football and
some other contact sport, 30% play football, and 40% play
other contact sports. If there are 200 athletes, how many
play neither football nor any contact sport.
Draw a two-way table of the data.
Solve for how many students (not percent) play neither
football or any contact sport.
A.P Statistics Released Question
reflecting knowledge of formula
Information Given: x  5 and s x  4
y  10 and s y  10
Choices
yˆ  8 . 5  0 . 3 x
yˆ   5 . 0  3 . 0 x
yˆ  5 . 0  2 . 5 x
yˆ  b 0  b1 x
b 0  y  b1 x
b1  r
sy
sx
yˆ  3 . 0 x
yˆ  10 . 0  0 . 4 x
Other side to Cumulative Probability worksheet
1.
2.
3.
4.
0.04734
0.38278
0.97175
0.15026
1. 0.114396
2 . 0114396
3. In 20 trials 12 successes is the same as 8 failures.
Also if a success is 0.7, then a failure is (1-0.7) = 0.3 .
H.W. Etc…
6.2 E #23 – 25
Look at both assignments: A.P. Practice of Ch. 5 and Ch.6
and One-Boy Family Planning
Decide which one you want to complete and print it for
February 6th (Monday)
February 2nd (Thursday) 6.3 Geometric Distribution and
Quiz on 6.1 and 6.2
February 6th (Monday) A.P. Statistics finished more details
on 6.3 and start on selected assignment
1st day of Ntbk Check
February 8th (Wendesday) Practice Ch. 6 Test and finish
selected assignment.
Ch. 6 Test on Friday February 9th!
Answers to Whiteboard Review
•
•
•
•
•
•
•
1) a
2) c
3) d
4)c
5) c
6) b
7) c
8) c
Bonus! Two-way table should
show that 70 athletes
are not in either football
or a contact sport.