Statistical inference — Question 4

QCAA 2021, Paper 2 · 1 mark

Q4 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 4

The mean time that visitors spend at an art exhibition is

39

minutes and the standard deviation is

6

minutes.

Determine the approximate probability that the mean time spent at the exhibition by a random sample of

35

visitors is between

38

and

40

minutes.

(A)

0.13

(B)

0.16

(C)

0.68

(D)

0.84

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

Worked solution

For

n=35

\bar X

has mean

39

and standard deviation

6/\sqrt{35}\approx1.014

. Thus

P(38<\bar X<40)=P(-0.986<Z<0.986)\approx0.676

, which rounds to

0.68

Selects option C.

[1 mark]

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

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