A continuous random variable X has cumulative distribution function F(x) = x^3/8 for 0 <= x <= 2. What is the median m of X? Give your answer to 3 decimal places.

Model answer

1.587

Also accepted: 1.59, cube root of 4

Explanation

The median satisfies F(m) = 0.5, so m^3/8 = 0.5, giving m^3 = 4 and m equal to the cube root of 4, which is approximately 1.587.

Derived from ZIMSEC Statistics Paper 2, November 2022, Q3

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