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IB Mathematics: Applications and Interpretation SL · 13.2: Probability Distributions · 13.2.5

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Binomial probabilities with the calculator Problem set B

Define X and state its distribution. Use the calculator's binomial pdf or cdf, and write the settings you used. Give probabilities to 3 significant figures.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. \(X \sim B(22, 0.35)\). Find

    1. (a) \(P(X = 9)\)
    2. (b) \(P(X \ge 11)\)
    3. (c) \(P(X < 6)\)

  2. \(X \sim B(5, 0.6)\). Complete the table of the probability distribution of X. Give each value to 3 significant figures.

    x012345P(X = x)??????

  3. Each of the 48 trees in an orchard independently bears fruit this year with probability 0.35. X is the number of trees that bear fruit.

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

In context

  1. A printer jams on 15% of mornings, independently from day to day. Over 30 mornings, X is the number of mornings it jams. Find the probability that the printer jams on

    1. (a) exactly 4 mornings
    2. (b) at least 7 mornings
    3. (c) fewer than 3 mornings

  2. A student tries a puzzle game 6 times. Each attempt independently succeeds with probability 0.35. X is the number of successful attempts.

    x0123456P(X = x)???????
    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 3 attempts succeed.

Stretch

  1. An archer hits the target with each arrow with probability 0.65, independently. She shoots 16 arrows. X is the number of hits.

    1. (a) Find the probability that the archer hits the target at least 13 times.
    2. (b) Find the probability that the archer hits the target fewer than 8 times.
    3. (c) Find the largest whole number k such that \(P(X \le k) < 0.05\).

jmaths.xyz · AI SL · 13.2.5 Binomial probabilities with the calculator