Warm-up6.2 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 Formulasvs. Probability Distribution Formulas

Probability DistributionBinomial Distribution

ixix

iix

px

pxu22 )( )1(2 ppn

npu

x

x

6.2 (Day 2) Binomial DistributionFinding the mean and SD

pnp

pnxE

x

x

1

)(

As n increases, the distribution becomes more normal.

Characteristics of BinomialDistribution:

Shape, Center and Spread

H.W. and quiz next block6.2 E #23-25

Be ready for a quiz on 6.1 and 6.2

You will be given the following formulas on theday of the quiz:

)1(

ondistributibinomialFor

)(E(x) 22x

pnpnk

puxxVarpx

x

ixixii

Conclusions from Student FeedbackA.P. Statistics

Good and should keep

• Printed Notes• Documents on Sharepoint• Clearly labeled daily schedule• Practice Tests• Collaborative Work• Student of the day!FYI: The calculator can be used on

all the exam. There is no non-calculator section.

Those of you that want access toA.P. Released Material, bring aflashdrive and come in duringBlock 7. I will be happy to give you files.

Changes and or/ ideas

• More A.P. type questions - I have incorporated A.P.

released Qs. - I will include more A.P. type

questions in a game or activity for each chapter.

• Reduce # of items on agenda• ½ the class likes activities and

other don’t. - Solution: differentiated

instruction, there will be days where you can chose to do an activity or A.P. type questions

Multiple Choice Practice on Probability

1) A binomial event has n = 60 trials. The probabilityof success on each trial is 0.4. Let X be the count ofthe successes of the event during the 60 trials. Whatare ?(a) 24, 3.79(b) 24, 14.4(c) 4.9, 3.79(d) 4.90, 14.4(e) 2.4, 3.79

(s.d)and xx

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) (d) (b) (e) (c)

3252 )6.0()4.0(

4151 )6.0()4.0(2

452 )6.0)(4.0(2

10

6

4

1

5

2

5

2

5

2

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) 341 )65.01)(65.0(

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 Questionreflecting knowledge of formula

45 xsandx 1010 ysandy

xy 0.30.5ˆ xy 0.3ˆxy 3.05.8ˆ

xy 5.20.5ˆ xy 4.00.10ˆ

x

y

s

srb

xbyb

xbby

1

10

10ˆ

Information Given:

Choices

Other side to Cumulative Probability worksheet

1. 0.047342. 0.382783. 0.971754. 0.15026

1. 0.1143962 . 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.6and 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 6.2February 6th (Monday) A.P. Statistics finished more details on 6.3 and start on selected assignment 1st day of Ntbk CheckFebruary 8th (Wendesday) Practice Ch. 6 Test and finish selected assignment. Ch. 6 Test on Friday February 9th!

Answers to Whiteboard Review

• 1) a 8) c• 2) c Bonus! Two-way table should• 3) d show that 70 athletes• 4)c are not in either football• 5) c or a contact sport.• 6) b• 7) c