Question 74029
Geometric and Binomial trials
Geometric: E(X)=1/p; SD(X)=square root of q/p^2
Binomial: E(X)=np; SD(X)=square root of npq 

1. in a bowling league, the mean score for men is 154 with a standard deviation(SD) of 9...for women it is a mean of 144 with a standard deviation of 12. at the end, they randomly pair men and women as opponets
a)what is the expected total score of men and women pairs?
For the men:
mean=np = 154; std=sqrt(npq)=9
So, std=sqrt(154q)=9
Square both sides to get 154q=81
q=81/154; therefore p=73/154
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For the women:
mean=np=144; std=sqrt12
So, std=sqrt(144q)=12
Square both sides to get 144q=144
q=1 and p=0
COMMENT: This does not make sense.
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b)what is the Standard Deviation of the sum of the pairs? 
If std=9, Var=81
If std=12, Var=144
std(men+women)=sqrt(81+144)= 15
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2. 18% of adults are smokers
a)they selected a few adults at random to find out if they are smokers. explain why this is a Bernoulli trial? 
Two possible outcomes: smoker or no smoker
Smoking among the people selected may not be independent but they
are less then 10% of the total population.
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b)how many people do you expect to ask to find a smoker?
??????? 
c)whats the probability that there are at least 8 smokers among a sample of 30 people? 
n=30,p=0.18,X>=8
If you have a TI calculator use [1- binomcdf(30,0.18,7)]=0.158...
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3. 70% of drivers wear seatbelts. there was a random sample of 500 drivers taken.
a)use a Binomial model to find the probablity that at least 350 drivers are wearing seatbelts?
n=500; p=0.7; X>=350
Use [1-binomcdf(500,0.7,349)]=0.522
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b)use a Binomial model to find the probablity that no more than 400 drivers are wearing seatbelts? 
X<=400
Use binomcdf(500,0.7,400)=0.999999
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Cheers,
Stan H.