Statistical inference — Question 3

QCAA 2020, Paper 2 · 1 mark

Q3 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 3

The masses of packages of cheese produced by a company are assumed to be normally distributed with a known mean of

\mu

grams and a standard deviation of

7.37

grams.

The packages of cheese are labelled to contain

500

grams.

Given there is a

25\%

probability that the mean mass of

20

randomly selected packages will be less than the labelled amount, the value of

\mu

(A)

498.89

(B)

500.25

(C)

501.11

(D)

504.98

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

Worked solution

\bar X\sim N(\mu,7.37/\sqrt{20})

. Since

P(\bar X<500)=0.25

, the corresponding standard normal value is about

-0.6745

. Thus

(500-\mu)/(7.37/\sqrt{20})=-0.6745

, giving

\mu\approx501.11

Selects option C.

[1 mark]

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

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