Binomial probabilities with the calculator Problem set A

\(X \sim B(18, 0.45)\). Find

1. (a) \(P(X = 8)\)
2. (b) \(P(X \ge 10)\)
3. (c) \(P(X < 7)\)

\(X \sim B(5, 0.25)\). Complete the table of the probability distribution of X. Give each value to 3 significant figures.

Each of the 36 plants in a greenhouse independently flowers in May with probability 0.25. X is the number of plants that flower in May.

1. (a) Write down the distribution of X.
2. (b) Find the mean of X.

A school lift is out of order on 8% of days, independently from day to day. Over a term of 40 school days, X is the number of days the lift is out of order. Find the probability that the lift is out of order on

1. (a) exactly 3 days
2. (b) at least 5 days
3. (c) fewer than 2 days

A nurse gives 6 patients a medicine. Each patient independently needs a second dose with probability 0.25. X is the number of patients who need a second dose.

1. (a) Complete the table of the probability distribution of X. Give each value to 3 significant figures.
2. (b) Find the probability that at least 2 patients need a second dose.

A basketball player makes each free throw with probability 0.72, independently. She takes 15 free throws. X is the number she makes.

1. (a) Find the probability that the player makes at least 12 free throws.
2. (b) Find the probability that the player makes fewer than 9 free throws.
3. (c) Find the largest whole number k such that \(P(X \le k) < 0.05\).