Final answer:
To calculate the expected value of the number of points Amos makes on two free throw shots, you need to find the probability of him making each shot. Using the binomial probability formula, you can calculate the probabilities of him making 0, 1, or 2 shots, and then find the expected value by multiplying each probability by the number of points for that outcome and summing them.
Step-by-step explanation:
To calculate the expected value of the number of points Amos makes when he shoots two free-throw shots, we first need to find the probability of him making each shot. Amos's free-throw shooting percentage is 57.5%, which means he makes the shot 57.5% of the time. Therefore, the probability of him making a free throw is 0.575.
Since he gets two free-throw shots, we can use the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of getting k successes (k made free throws), n is the number of trials (2 shots), p is the probability of success (0.575), and C(n,k) is the number of combinations.
Using the formula, we can calculate:
P(X=0) = C(2,0) * (0.575)^0 * (1-0.575)^(2-0) = 0.1815625
P(X=1) = C(2,1) * (0.575)^1 * (1-0.575)^(2-1) = 0.4540625
P(X=2) = C(2,2) * (0.575)^2 * (1-0.575)^(2-2) = 0.364375
The expected value is then calculated as:
Expected Value = (0 * P(X=0)) + (1 * P(X=1)) + (2 * P(X=2))
Expected Value = (0 * 0.1815625) + (1 * 0.4540625) + (2 * 0.364375) = 1.1828125
Rounding to two decimal places, the expected value of the number of points Amos makes when he shoots two free-throw shots is 1.18 points.