Statistical inference — Question 9

QCAA 2022, Paper 1 · 1 mark

Q9 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 9

A random variable

X

is normally distributed with a mean of

36

and a standard deviation of

4

The respective mean and standard deviation of the distribution of

\bar X

from repeated random samples of size

9

are

(A)

4

and

\frac49

(B)

4

and

\frac43

(C)

36

and

\frac49

(D)

36

and

\frac43

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

The sampling distribution satisfies

E(\bar X)=\mu=36

and

\sigma_{\bar X}=\sigma/\sqrt n=4/3

Selects option D.

[1 mark]

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

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