Statistical inference — Question 9

QCAA 2023, Paper 2 · 1 mark

Q9 · 2023 · Technology-activeSimple familiar1 mark

QUESTION 9

The time in minutes between the arrival of customers at a certain shop is assumed to be a random variable

X

with an exponential distribution that has the probability density function

f(x)=\begin{cases}0.12e^{-0.12x},&x\ge0\\0,&\text{otherwise}\end{cases}

. A customer arrives at the shop. The probability that the next customer arrives within 30 to 60 seconds, to the nearest percent, is

(A)

(B)

(C)

(D)

11%

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

Worked solution

Thirty to sixty seconds is

0.5

1

minute. Hence

P(0.5<X<1)=e^{-0.12(0.5)}-e^{-0.12(1)}\approx0.0549

, or

5\%

to the nearest percent.

Selects option B.

[1 mark]

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

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