Practise questions | Salam Academy

SA-9709-P6-CR3-0022 marksL2 StandardCalculatorMedian

f(x)=\tfrac38x^2

for

0\le x\le2

, and

0

otherwise. Find the median, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0014 marksL2 StandardCalculatorBinomial tests

A coin is suspected of being biased towards heads. In

12

throws it shows

10

heads. Test at the

5\%

level. Give

P(X\ge10)

under

H_0

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0024 marksL2 StandardCalculatorPoisson tests

Accidents at a junction occur at an average of

4

per day. After changes, there is

1

accident on a randomly chosen day. Test at the

5\%

level whether the rate has fallen. Give

P(X\le1)

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0034 marksL2 StandardCalculatorTests for a mean

A population has standard deviation

5

. A random sample of

36

has mean

51.8

. Test

H_0:\mu=50

against

H_1:\mu\ne50

at the

5\%

level. Give the test statistic and conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT1-0034 marksL2 StandardCalculatorPoisson tests

A shop received an average of

6

complaints a week. After new staff training, a randomly chosen week has

2

complaints. Test at the

5\%

level whether the rate of complaints has fallen. Give

P(X\le2)

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0023 marksL2 StandardCalculatorTests for a mean

A population has standard deviation

8

. A random sample of

64

has mean

52.2

. Test

H_0:\mu=50

against

H_1:\mu\ne50

at the

1\%

level. Give the test statistic and your decision.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0042 marksL2 StandardCalculatorTests for a mean

A population has standard deviation

12

. A test of

H_0:\mu=80

against

H_1:\mu>80

uses a sample of

36

at the

5\%

level. Find the critical value of

\bar x

, correct to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT3-0012 marksL2 StandardCalculatorErrors

H_0:p=0.4

,

H_1:p>0.4

, with

n=10

.

H_0

is rejected if

X\ge8

. Find the probability of a Type I error, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT3-0023 marksL2 StandardCalculatorErrors

For the test in the previous question (

n=10

, reject

H_0:p=0.4

if

X\ge8

), the true value of

p

is

0.7

. Find the probability of a Type II error, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT3-0052 marksL2 StandardCalculatorErrors

H_0:\lambda=3

,

H_1:\lambda>3

, where

X\sim\text{Po}(\lambda)

.

H_0

is rejected if

X\ge7

. Find the probability of a Type I error, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-G014 marksL2 StandardCalculatorBinomial tests

A treatment succeeds for

30\%

of patients. In a trial of a new method on

20

patients, only

2

succeed. Test at the

5\%

significance level whether the success rate is lower with the new method. Give the probability you compare (3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-LC-0023 marksL2 StandardCalculatorNormal combinations

X\sim N(50,9)

and

Y\sim N(30,16)

are independent. Find

P(X+Y>85)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-LC-0102 marksL2 StandardCalculatorMultiples vs sums

X\sim N(10,4)

. Find

\text{Var}(3X)

and

\text{Var}(X_1+X_2+X_3)

, where the

X_i

are independent observations of

X

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-LC2-0034 marksL2 StandardCalculatorTotals

Apple masses are

N(150,100)

grams. A box holds

12

randomly chosen apples. Find the probability that the total mass exceeds

1850

g, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-LC3-0023 marksL2 StandardCalculatorNormal combinations

X\sim N(12,1)

and

Y\sim N(10,8)

are independent. Find

P(X>Y)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-LC3-0033 marksL2 StandardCalculatorNormal combinations

Jar masses are

N(350,16)

g and lid masses are

N(20,1)

g, independently. Find the probability that a jar with its lid weighs more than

375

g, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0023 marksL2 StandardCalculatorProbabilities

X\sim\text{Po}(2.5)

. Find

P(X\ge3)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0033 marksL2 StandardCalculatorScaling λ

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

4

per hour. Find the probability of exactly

3

calls in a

30

-minute period, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0053 marksL2 StandardCalculatorPoisson for binomial

X\sim B(200,0.015)

. Use a suitable approximation to find

P(X=4)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO-0113 marksL2 StandardCalculatorScaling λ

Faults occur in cloth at random at an average of

0.4

per metre. Find the probability of at least

2

faults in a

5

m length, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

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