px(1 - p)n-x. Let X ~ Bin(8, 0.55).
a.) Find P(X = 3).
0.172
b.) Explain what a.) means in words (plain english).
If Bin(8,0.55) was our distribution, then the probability of three successes would be approximately 17.2%.
c.) Find P(X ? 2).
0.98192
d.) What is the mean and variance of this distribution?
Mean = 4.4
Variance = 1.98
2.) Let�s draw a tree diagram. Pretend that we went to a party and that twenty percent of the people are male. Then, of the males, fifteen percent are married. Of the females, twenty-five percent are single. Pretend also that there are only single and married, only male and female.
a.) Draw a tree diagram to represent the above situation.
A tree diagram
b.) What is the probability that someone is single?
0.37
c.) Of the people that are married, what is the probability that someone is female?
0.952
d.) Of the people that are male, what is the probability that someone is single?
0.85
3.) Let S= {a,b,v,s,r,t,1,2,3,4}. Let A={1,2,a,v,s} and let B= {a,b,v,s,r,t}.
a.) What is A U B?
{1,2,a,b,v,s,r,t}
b.) What about A ? B?
{a,v,s}
c.) What is B ? �?
{�}
d.) What is (� U S) ? A?
A
4.) Let X be distributed as follows:
X 1 3 5 7
P(x) 0.05 0.15 0.75 0.05
a.) Find E(X).
4.6
b.) Find the standard deviation of X, St Dev(X). {Hint: Var(X) = E(X2) � (E(X))2}
Var = 1.44
Std Dev = 1.2