Statistical inference — Question 1

QCAA 2021, Paper 2 · 1 mark

Q1 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 1

The time taken to complete orders at a pizza store is normally distributed with a mean time (

\mu

) of

10

minutes.

The owner of the pizza store records the time taken to complete orders for a random sample of

20

pizzas each day over a

30

-day period. From this data, an approximate

90\%

confidence interval for

\mu

is calculated at the end of each day.

How many of these confidence intervals would be expected to contain

\mu

(A)

3

(B)

18

(C)

27

(D)

30

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

Worked solution

90\%

confidence procedure captures the true mean in about

90\%

of repeated samples. Over

30

intervals, the expected number containing

\mu

0.90\times30=27

Selects option C.

[1 mark]

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

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