according to census bureau data, 20% of employed women have never been married. Take a random sample of employed women and observe their marital status.

a. Is X normal, binomial, or gemetric
b) If 10 employed women are selected at random, what is the probability that 3 or fewer have never been married?
c) If 10 employed women are selected at random, what are the mean and standard deviation

Question

according to census bureau data, 20% of employed women have never been married.  Take a random sample of employed women and observe their marital status.

a. Is X normal, binomial, or gemetric
b) If 10 employed women are selected at random, what is the probability that 3 or fewer have never been married?
c) If 10 employed women are selected at random, what are the mean and standard deviation

anonymous · Answer

have you taken a random sample of employed women?

anonymous · Answer

I didn t have everything written down.

anonymous · Answer

x is distributed according to the binomial distribution.

for n = 10 sampled 
expected mean is np = 10 (0.2)
expected standard deviation is sqrt(npq) = sqrt(10 x 0.2 x 0.8)

mathmale · Answer

Nice work, DWC.  Would you mind explaining your reasoning in regard to how you decided that this is a binomial distribution and not a normal one?  (I agree with your conclusion, but would like to know how you got to it).

anonymous · Answer

Binomial comes from underlying situation where something either is (p) or is not (q), and the entities are discrete units. Normal distribution has continuous variables rather than discrete. Normal is good approximation to the binomial when you have large sample sizes, if I recall corectly.