Exam-Style Question on Normal Distribution
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 566. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.
The time in minutes taken to drive through a city at different times of the day can be modelled by a normal distribution with mean of 45 and standard deviation of 12. A commuter will be late for work if it takes more than an hour to drive through the city.
(a) Find the probability that the commuter is late for work.
(b) Estimate the number of days on which the commuter was late from random sample of 100 days.
(c) Given that the commuter is not late, find the probability that the cross-city journey took less than 25 minutes.
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