Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-IAL-S2-CD-0121 markL1 FoundationCalculatorChoosing & correcting

X

is binomial and

Y

is its normal approximation.

P(X<15)

is approximated by

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD2-0012 marksL1 FoundationNon-calculatorNormal approximations

X\sim B(100,0.5)

is approximated by

Y\sim N(\mu,\sigma^2)

. Write down

\mu

and

\sigma^2

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-Q021 markL1 FoundationCalculatorNormal approximations

A normal approximation to

\text{Po}(\lambda)

is suitable when

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-Q031 markL1 FoundationCalculatorChoosing & correcting

With a normal approximation

Y

P(X\ge8)

becomes

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0084 marksL2 StandardCalculatorNormal approximations

X\sim\text{Po}(25)

. Use a normal approximation to find

P(X>30)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0101 markL2 StandardCalculatorChoosing & correcting

X\sim B(200,0.02)

. The most suitable approximation to the distribution of

X

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0111 markL2 StandardCalculatorChoosing & correcting

X\sim B(60,0.5)

. The most suitable approximation to the distribution of

X

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD2-0024 marksL2 StandardCalculatorNormal approximations

X\sim\text{Po}(50)

. Use a normal approximation to find

P(X\le45)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0064 marksL3 ExamCalculatorNormal approximations

X\sim B(80,0.3)

. Use a suitable approximation to find

P(X\le20)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0074 marksL3 ExamCalculatorNormal approximations

X\sim B(50,0.4)

. Use a normal approximation to find

P(X\ge25)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0094 marksL3 ExamCalculatorNormal approximations

X\sim\text{Po}(40)

. Use a normal approximation to find

P(35\le X\le45)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S2-CD-0136 marksL4 ChallengingCalculatorNormal approximations

Calls arrive at a help desk at random, at an average rate of

3

per hour. (i) Write down the distribution of the number of calls

X

in an

8

-hour day. (ii) Use a normal approximation to find the probability that there are at least

30

calls in a day, to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme