Question

Suppose you are flipping a coin, but this particular coin is not fair. It has a 0.68 probability to land on heads, instead of the usual .5. Suppose that you flip the coin 7 times and let X represent the number of times it lands on heads.

Find E(X) (round your answer to 2 decimals)
Find the standard deviation of X (round your answer to 2 decimals)
Find the probability X is at least 3 (round your answer to 2 decimals)

Answer 1

The expected value of X is 4.76 and the standard deviation of X is 1.13. The probability that X is at least 3 is 0.722.

Step-by-step explanation:

To find the expected value of X, which represents the number of times the coin lands on heads, we multiply the probability of a head (0.68) by the number of flips (7). This gives us a mean or expected value of 0.68 * 7 = 4.76.

To find the standard deviation of X, we use the formula sqrt(n * p * q), where n is the number of flips, p is the probability of a head, and q is the probability of a tail. Plugging in the values, we get sqrt(7 * 0.68 * 0.32) ≈ 1.13.

To find the probability that X is at least 3, we add up the probabilities of X being 3, 4, 5, 6, or 7. Using a binomial probability calculator, we find this probability to be approximately 0.722.