Tossing a pair of coins

Question

We have a white coin, for which P(Heads)=0.4 and a black coin for which P(Heads)=0.6. The flips of the same or of different coins are independent. For each of the following situations, determine whether the random variable N can be approximated by a normal. If yes, enter the mean and variance of N. If not, enter 0 in both of the corresponding answer boxes.

1. Let N be the number of Heads in 100 tosses of the white coin.

2. Let N be the number of Heads in 100 coin tosses. At each toss, one of the two coins is selected at random (either choice is equally likely), and independently from everything else.

3. Let N be the number of Heads in 50 tosses of the white coin followed by 50 tosses of the black coin (for a total of 100 tosses).

4. We select one of the two coins at random: each coin is equally likely to be selected. We then toss the selected coin 100 times, independently, and let N be the number of Heads.

mean and variances ???

Answer 1

1. mean = 40, variance = 24

2. mean = 50

3. mean = 50, variance = 24

4. mean = 0, variance = 0

the variance for question 2 is missing...Help us out, please!!

Answer 2

variance for q2?

Answer 3

2. mean 50, variance 25