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9.03 Centre and spread of continuous random variables

Interactive practice questions

Consider the following.

a

Select the option which shows two distributions with the same expectation.

A

B

C

D
b

Consider the graphs of the two distributions below.

Which of the following scenarios could be modelled by these two distributions?

The length of two species of fish A and B which have the same average length, but where the length in of species B varies more than in the other.

A

The battery life of two different brands of phones A and B, where phone A has a longer average battery life but the variation in battery life among the two phones is the same.

B
Easy
< 1min

Consider the following.

Easy
< 1min

Consider the probability density function $p\left(x\right)=\frac{1}{40}$p(x)=140 when $10\le x\le50$10x50.

Easy
1min

Consider the probability density function $p\left(x\right)=\frac{3}{160}\left(x^2+4x\right)$p(x)=3160(x2+4x) when $0\le x\le4$0x4.

Medium
2min
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Outcomes

4.4.1.3

calculate the expected value, variance and standard deviation of a continuous random variable in simple cases

4.4.1.4

understand standardised normal variables (z-values, z-scores) and use these to compare samples

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