Statistical inference — Question 10

QCAA 2022, Paper 2 · 1 mark

Q10 · 2022 · Technology-activeSimple familiar1 mark

QUESTION 10

In a town, the mean number of residents per household is 3.79 people with a standard deviation of 1.47 people. Using a random sample of 45 households from the town, determine the probability that the mean number of residents per household will be more than 4.

(A)

0.17

(B)

0.33

(C)

0.83

(D)

0.96

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

Worked solution

For

n=45

, the sampling distribution has mean

3.79

and standard error

1.47/\sqrt{45}\approx0.219

. Thus

z=(4-3.79)/0.219\approx0.958

, so

P(\bar X>4)=1-\Phi(0.958)\approx0.169\approx0.17

Selects option A.

[1 mark]

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

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