# Exam-Style Question on Normal Distribution

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 371. This question is similar to one that appeared on an IB AA Standard paper (specimen) for 2021. The use of a calculator is allowed.

The length, $$X$$ minutes , of a certain category of online video is normally distributed with a mean of 28.

The probability that $$X$$ is less than 20 is 0.213.

(a) Find $$P(20 \lt X \lt 28)$$.

(b) Find the standard deviation of $$X$$.

(c) Hence, find the probability that a video selected at random from this category lasts longer than 33 minutes

(d) How many of these videos could be expected to last longer than 33 minutes?

(e) Find the probability that exactly two of these videos last longer than 33 minutes.

(f) A video selected at random from the complete online collection of videos in this category has a running time of less than 20 minutes. Find the probability that its length is between ten and fifteen minutes.

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