Statistical inference — Question 4

QCAA 2021, Paper 1 · 1 mark

Q4 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 4

The number of sunflower seeds in each packet produced by a company is known to be normally distributed with a standard deviation of

100

. A worker counts the number of seeds in a random sample of four packets and calculates the sample mean.

Based on this sampling, the standard deviation of the distribution of the sample mean is

(A)

25

(B)

50

(C)

75

(D)

100

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

Worked solution

The standard deviation of the sample mean is

\sigma_{\bar X}=\sigma/\sqrt n=100/\sqrt4=50

Selects option B.

[1 mark]

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

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