Question

Let X be a binomial random variable with p=0.5 and n=10. Calculate the following Probabilities from the binomial probability mass function. Round your answers to four decimal places.

a.) P(X<_ 2)

b.) P(X=4)

c.) P(X>8)

d.) P(3<_ X<5)

Answer 1

To calculate the probabilities, we use the binomial distribution formula based on the given parameters.

Step-by-step explanation:

To calculate the probabilities from the binomial probability mass function, we can use the binomial distribution formula. Let X be a binomial random variable with p=0.5 and n=10.

a) To find P(X ≤ 2), we need to calculate P(X = 0) + P(X = 1) + P(X = 2). Using the binomial distribution formula, we can calculate these probabilities and add them up to get the answer.

b) To find P(X = 4), we use the binomial distribution formula to calculate this specific probability.

c) To find P(X > 8), we need to calculate P(X = 9) + P(X = 10). Using the binomial distribution formula, we can calculate these probabilities and add them up.

d) To find P(3 ≤ X < 5), we need to calculate P(X = 3) + P(X = 4). Using the binomial distribution formula, we can calculate these probabilities and add them up to get the answer.