Sunday

March 29, 2015

March 29, 2015

Posted by **AMber** on Saturday, August 4, 2012 at 10:03am.

a) Exactly 10 have had an adult beverage

b) At least 6 have had an adult beverage

c) At most 8 have had an adult beverage

d) At most 1 has had an adult beverage.

- stats -
**MathMate**, Saturday, August 4, 2012 at 1:37pmHere are some properties of the experiment:

1. Each trial is Bernoulli (i.e. yes/no)

2. Number of trials is fixed.

3. probability of success does not vary from trial to trial.

4. each trial is independent of the others (assumed random sample).

All these point to the binomial distribution with N=10, p=0.95, q=(1-0.95)=0.05, and success="have had at least one adult beverage".

P(X=i)=(N,i)p^i q^(N-i)

and (N,i) = number of ways to choose i objects from N distinct objects.

(N,i)=N!/(i!(N-i)!)

a). N=10, i=10, p=0.95, q=0.05

P(X=10)=(10,10)0.95^10 0.05^0

=1*0.95^10*1

b) At least 6 => X=6,7,8,9,10

So

P(X≥6)=∑P(X=i), i=6 to 10

c) At most 8 => X=1,2,3...8

=> X≠9 and X≠10

We can use the identity

P(X≤8)=∑P(X=i), i=1 to 8

=1-P(X≥9)

=1- [∑P(X=i), i=9 to 10]

which simplifies the calculations.

d) at most 1 => X=0 or X=1.

**Answer this Question**

**Related Questions**

statistics - 1.a person selects a card from a deck .it is a red card ,he wns 1$....

statistics - if 20% of the people in a community use the library in one year, ...

math - R. H. Bruskin Associates Market Research found that 30% of Americans do ...

PROBABILITY - R. H. Bruskin Associates Market Research found that 40% of ...

Maths - College Education and Business world success R. H. Bruskin Associates ...

statistics - Data shows that 88% of the people in a certain population are right...

statistics - If 20% of the people in a community use the emergency room at a ...

math - if 20%of the people in school use the emergency room at the hospital in ...

STATISTICS - From a group of 12 people, you randomly select 3 of them. Find the ...

STATISTICS - From a group of 12 people, you randomly select 3 of them. Find the ...