Chapter 1. Tutorial: Binomial Distributions - Definition

1.1 Problem Statement

{30020,40111,52619,41510,72114,83261,10123,20371,02480,34205}
rand(0,9)
@table[$tableindex]
{Jung,Adelaja,Yajima,Fox,Modur,Jung,Adelaja,Jung,Jung,Burke}
@table01[$tableindex]
{Gupta,Jung,Jung,Jung,Hernandez,Gupta,Jung,Gupta,Gupta,Jung}
@table02[$tableindex]
{Mazzeo,Gao,Mani,Huo,Barnes,Barnes,Rodriguez,Barnes,Sanchez,Barnes}
@table03[$tableindex]
{Barnes,BArnes,Barnes,Barnes,Ding,Ding,Barnes,Ding,Barnes,Ding}}
@table04[$tableindex]

There are 5 conditions for a binomial distribution to be an appropriate model for a random variable:

1. There are a fixed number n of observations

2. The n observations are independent of each other.

3. Each observation falls into one of two categories which are arbitrarily called “success” and “failure”.

4. The random variable X counts the number of “success”.

5. The probability of success p is the same for all observations.

For each situation below identify the attributes of the binomial distribution (if applicable) or identify why the following is not a binomial distribution.

1.2 Step 1

questions

Count the number of heads in 5 flips of a fair coin.

Question 1.1

n is pB9riSzaspz6PYCmwb3oymhqeZAySvi0QbVhoo1pVIfwM541xnegsU0s0Og=

Correct.
Incorrect.

Question 1.2

Each coin’s outcome d7FMb4RH1Z8539k+oiW8khTHEO4xChWcYBa8pT/1AEo2XQhfF/xr15bq+fWwkJEtwZmXY0B0xZCGnD9RKfRAubOp7FclBq61.

Correct.
Incorrect.

Question 1.3

There are XvVM00l89Is= outcomes for each flip with a ____ q6fFEtbkgG3mr3T5JenhTA== being defined as a success.

Correct.
Incorrect.

Question 1.4

We are counting E0L/Md/ZjF/VIOg6SJqL55e7xcNtnWsOoDZghovv3EQx2Q/IiXo+J2zrrZgrfwMC1VMTljtDOFYAqyU+W+63PpvNM+INBJu/UvSBZ5UWoBoJotj+FxiFudyAqdFvzCwyPYxC4w==.

Correct.
Incorrect.

Question 1.5

The probability of success is (give your answer in decimal form) ot+qaZUmHUo= which is s3wstqOIcq40gTq3J6rNPawZCcvowUfe for each trial.

Correct.
Incorrect.

Question 1.6

This imf3zWu5ZCEoGIrfhClNhw== a binomial situation.

Correct.
Incorrect.

1.3 Step 2

Count the number of boys in sets of identical twins.

Question 1.7

n is GjplM3//U4/ohZRIgetSeH2Pj8xcjp1ZRt1LtXhh1xdctkqx.

Correct.
Incorrect.

Question 1.8

The second child’s sex Nyod7h8SyoJBKJb3/Q07aMZ06urV/salFvZ3gk8i4dZ2W/VbgnR3PkCg8sacNjg/SDz2lci1aluLYtJvf+Xpkb6Fx0yBeU7wQ8zkvHkc+W2UgGp/3Hae4A==.

Correct.
Incorrect.

Question 1.9

There areXvVM00l89Is= outcomes for each count with a EW1K8BOKOsadqSt7WH3fYQ== being defined as a success.

Correct.
Incorrect.

Question 1.10

We are counting YmfaWl0Ed+Gjirwu1T/pp+s+OEl0H56BeEUZbVtf+FdTCeISEYY2i/vJD9UAa+wA96g1cW/UX9Pdjm0e.

Correct.
Incorrect.

Question 1.11

The probability of success is (give your answer in decimal form) ot+qaZUmHUo= for the first child; the probability of success is CE7qYTsMlWMQQBr2EgzY1zkURxjEcVsG22rF+fr6ba3/L3xE1UHv+8UQTAw5O1TvFHS4IRspL+RJ/dW5ZBgt+TNoOOh8zhDk for the sex of the second child.

Correct.
Incorrect.

Question 1.12

This AgprdJo46NHaz28x2bF68g== a binomial situation.

Correct.
Incorrect.

1.4 Step 3

Count the number of questions correct in a multiple choice quiz of 20 questions where every question has 5 possible options and you are just guessing for every question.

Question 1.13

n is nz5GAb7mp4WQmfa8ikAxew0+f0qTukyQmjUZ93/zgeVPSbQ6.

Correct.
Incorrect.

Question 1.14

Getting a question correct /ADRSkoNnqkppfVSxmzYbo9pJwQ7pFZ40HKpg7eKMdSHPKieIWgbg129zqIoTxBrJhJKTs0otbBsWbF9ruLkLjC+C6r2dXBSHkK5ZyxNYyQ=.

Correct.
Incorrect.

Question 1.15

There are n9PEn8r8T+NPOQBL outcomes for each question with a success defined as PN5l0U+Xts4QDPB9c0Q7FURLpVntnYVG67PQHVBmG2BW4GSQEWIqL0kXeFj5f/go5HzNZ804elaStUuGvzQsiDIYKyWfJQSW4zUt/OIeJb0/5gZXqArk2jIayyrYySi+rXurrrJWriBz8Q3gyFmFjQ==.

Correct.
Incorrect.

Question 1.16

+YLavDrBTdxaZM0ORUS+EFwf11HMRcN2lAnpX6HS9vSA0U4ojqoOSJjm/EpCnyesb4P/6THR5Nr6Iim1Cy9Mk6Geb6mwwqPPTw18VjQCve4bB76jUYknGlc+I/5abUSpkPBZJJOGdyqINvyfZD52gPJwyxaWHd1g
Correct.
Incorrect.

Question 1.17

xyxLoxl5zZbtCt2vffJBrIH+yItTeiopZzD8W5Rkffi/dD7nwkqyRELdLf48z4XvIxN5Qunyr5DdfNSoVBQjqRC9ABxkuyp45mRzsjhiLsLd+UasJfJedyet9Q8/tL/nqUc0nw==
Correct.
Incorrect.

Question 1.18

This imf3zWu5ZCEoGIrfhClNhw== a binomial situation.

Correct.
Incorrect.

1.5 Step 4

Count the number of months until an individual wins the jackpot in the Pick-4 lottery, if he buys one lottery ticket per month, and plays the same 4 numbers each time.

Question 1.19

n is IsMClbBH2LiZCfsYnK8YFINBtj+A/2mjINl86zzCUjfwmaxQ1DGkEA==.

Correct.
Incorrect.

Question 1.20

Winning the jackpot in the lottery in any month RGEXTNl3xnq6zyR0mBZZwA1s6xUmXHOnsoJJbMAN17DMboKpeegCD77DiqDWbjC5RTBpxmDnb+qsSic12P1YI42G2l4+T6yAWM0wNg==.

Correct.
Incorrect.

Question 1.21

There are XvVM00l89Is= outcomes for each month with a success defined as cY0Nvs2M4RIRySoH0fTrigjRBAC62O9ThWzk34NkhoUT2ynS/d1Y+ICbrJx3Dx7PORJbqYk1MRIR6I3XQRyq+9S3wYvMht2YGZrpIC6isz8J1i8iXTM+QnFvT1XxhtNLK6fXzyxwFGSk87Q4.

Correct.
Incorrect.

Question 1.22

We are counting nPGri0w8fCuqkzBEWaifnR0s5eMuHxnQRAx4Nt0Z2tKLE3+e+KmypdliCzPW/1NrEKhswGX8ze7ObUIk+ThDjPhQ5k0IhU30lc+lyosN4yF9S/Ue/loXmIUOm1szocfm6qKPAo3JMdjcuPUBfxRWyJ7HEk8u6keh.

Correct.
Incorrect.

Question 1.23

The probability of success is ____ PODaucPTsbbO/tYiKN/B+sBaEKFfmo0WQyN6pz2sUFrjWA0RdqJzRGkx7TeRin/mnw+lUMK5sPYgTEep.

Correct.
Incorrect.

Question 1.24

This AgprdJo46NHaz28x2bF68g== a binomial situation.

Correct.
Incorrect.