Tuesday

March 3, 2015

March 3, 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**

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

StatIstics - "Household size" is defined as the number of people living in a ...

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

math - at breakfast buffet, 93 people chose coffee for there beverage and 47 ...

Calculus Help? - I have no idea where to start? A survey of one thousand people ...

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

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

Calculus - A survey of one thousand people found that 70% of the people have a ...

Calculus Check - A survey of one thousand people found that 70% of the people ...

Cacluluc CHECK - A survey of one thousand people found that 70% of the people ...