Question 3

Probability

In answering each step / question (i, ii, iii, etc), I want evidence that you know what is relevant, what code or functions are appropriate and their correct use. So obviously you show and use functions correctly, but also briefly explain what you did.

(i) For a certain type of passenger aircraft, it is known that a particular air-conditioning problem occurs on 59% of all flights. What is the probability that four of the next five flights today, will require an air-conditioning specialist to be available?

(ii) For the above step (i), produce a plot showing the distribution of probabilities for today’s five flights. Briefly explain what the plot shows. Make the plot worthy of inclusion in a business report.

(iii) The probability of a childhood leukaemia patient having a relapse, within the first five years after successful treatment, is known to be 39.5%. For twelve patients who have recently completed treated, what is the probability that either 3, 4, 5, 6, 7, 8, 9 or 10 will have a relapse?

(iv) Produce a plot showing the distribution of probabilities for relapses for the above twelve patients, in step (iii), having a relapse. Briefly explain what the plot shows. Make the plot worthy of inclusion in a business report.

(v) A motorway has seven trucks for responding to calls for assistance. On average, five trucks are simultaneously involved in calls for assistance. What is the probability that more than seven simultaneous calls for assistance may occur?