Mathematical Methods — Question 4

QCAA 2022, Paper 1 · 1 mark

Q4 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 4

The weekly amount of money a company spends on repairs is normally distributed, with a mean of

\char36 1200

and a standard deviation of

\char36 100.

Given that

P(Z\le-2.5)=0.0062

and

P(Z>1)=0.1587

, where

Z

is a standard normal random variable, determine the probability that the weekly repair costs will be between

\char36 950

and

\char36 1300.

(A)

0.6525

(B)

0.6587

(C)

0.8351

(D)

0.8413

ABCD

WORKED SOLUTION

1 mark

ANSWER

C —

0.8351

Worked solution

The bounds correspond to

z=-2.5

and

z=1

. Hence

P(950<X<1300)=P(Z<1)-P(Z\le-2.5)=(1-0.1587)-0.0062=0.8351

, so C.

Selects option C.

[1 mark]

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