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Continuous random variables and the normal distribution — Question 372

Original QCE Vault practice · 4 marks

Q372 · Practice questionTechnology-freeSimple familiar4 marks

QUESTION 372 (4 marks)

The histogram models a viewing time XX minutes. Its vertical axis is relative frequency density, and values within each class interval are modelled as uniform. The three class intervals are [0,1)[0,1), [1,3)[1,3) and [3,6][3,6].
Relative frequency density histogram: height 0.2 on [0,1), 0.25 on [1,3), and 0.1 on [3,6]; zero elsewhere.
a)
Verify that the histogram can represent a probability density.
[1 mark]
b)
Determine P(1.5<X<4)P(1.5<X<4).
[2 marks]
c)
In 400400 independent observations from this model, determine the expected number with 1.5<X<41.5<X<4.
[1 mark]
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