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Probability Distributions · Part 2 of 3
6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on this part of the standard, grouped by the 2 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A basketball player makes 65% of free throws. In 12 attempts, find the probability she makes exactly 9, and the mean number made.
A seed company claims 92% germination. A gardener plants 40 seeds and only 32 germinate. Calculate the probability of 32 or fewer germinating if the claim is true, and comment on the claim.
An airline knows that 8% of passengers with bookings fail to turn up. It sells 265 tickets for a 250-seat flight. Find the probability that more passengers turn up than there are seats, and advise the airline on its overbooking policy.
Potholes occur at an average rate of 2.5 per kilometre on a rural road. Find the probability of exactly 3 potholes in one kilometre, and the standard deviation.
A bakery sells an average of 18 pies per hour. Find the probability that fewer than 5 are sold in a 15-minute period, and explain why the Poisson model may not hold across a whole day.
A hospital emergency department is designing its overnight staffing. Arrivals average 4.5 per hour between midnight and 6am. A manager argues that since 6 hours × 4.5 = 27 arrivals are expected and one doctor can see 5 patients per hour (30 over the shift), one doctor is sufficient. Evaluate this reasoning.