Statistical inference — Question 9

QCAA 2024, Paper 2 · 1 mark

Q9 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 9

Random variable

X

has an exponential distribution with the probability density function

f(x)=\begin{cases}\dfrac15e^{-x/5},&x>0\\0,&\text{otherwise}\end{cases}

. Given that

P(0\le X\le k)=0.5

, determine

k

(A)

0.10

(B)

0.69

(C)

2.03

(D)

3.47

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

P(X\le k)=1-e^{-k/5}=0.5

, so

e^{-k/5}=0.5

and

k=5\ln2\approx3.47

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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