two balls are randomly selected with replacement from a jar that contains seven red and three white balls. The number x of red balls is recorded.

Question

If the experiment is binomial, give the values of n and p. (If the experiment is not binomial enter NONE.)

Answer 1

p = Pr(red) q = P(white)- 1-p n = r+w = 7+3 = 10

np = mean = E(x)

npq = np(1-p) = np-np^2 = variance = Var(x)

sqr(npq) = standard deviation of x

Answer 2

Remember the conditions for the binomial distribution:

The trials must be independent. (You are replacing the balls, so think about what that means regarding whether the trials are independent.)

The outcomes of each trial can be classified as "success" or "failure". (We're interested in the number of red balls specifically, so....)

The random variable measures the total number of successes. (It does measure the total number of red balls drawn.)

The trials must be identically distributed. (Again, you're replacing the balls.)

In the binomial distribution, n represents the number of trials (the problems tells you that number) and p represents the probability of a success (given 7 red and 3 white, you can calculate p without too much trouble.)