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Statistical inference — Question 14

QCAA 2020, Paper 2 · 5 marks

Q14 · 2020 · Technology-activeSimple familiar5 marks

QUESTION 14 (5 marks)

The time, tt (months), that it takes before a phone owner cracks the screen on their phone can be modelled by an exponentially distributed random variable with probability density function f(t)={0.16e−0.16t,t≥0,0,otherwise.f(t)=\begin{cases}0.16e^{-0.16t},&t\ge0,\\0,&\text{otherwise.}\end{cases}
a)
Show that f(t)f(t) is a probability density function.
[1 mark]
b)
Determine the probability that a phone owner cracks the screen on their phone within 1 year.
[2 marks]
c)
Three-quarters of phone owners take between 1 and mm months to crack the screen on their phone. Determine the value of mm.
[2 marks]
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