SOLUTION: 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 scor

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 qith 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 of men and women pairs?
b)what is the Standard Deviation of the sum of the pairs?

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?
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?

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?
b)use a Binomial model to find the probablity that no more than 400 drivers are wearing seatbelts?

im very lost on these problems so if you could help, id be so greatful!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
--------------
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.
--------------------

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
--------------

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.
-------------
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...
-------------

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
--------------------

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
---------
Cheers,
Stan H.

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