june 2014 (r) ma - s1 edexcel

8/17/2019 June 2014 (R) MA - S1 Edexcel

1/8

1.

st+

(A)

The

discrete

random

variable

xhas probability

distribution

(a)

Show

that

p

:

0.2

Find

(b)

E(ro

(c)

F(0)

(d)

P(3x+2>s)

Given

that

Yar(X)

:

1

3.35

(e)

find

the

possible

values

of

a

such

thatyar(aX+

3)

:

53.4

(2)

Q)

(1)

Q)

(2)

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2/8

The discrete

random variableXhas

probability

distribution

P(X:r)

:

+

x:1,2,3,

... 10

l0

Write down

the name

given

to this distribution.

Write

down the

value of

o

P(x:

10)

(ii)

P(x<

l0)

The

continuous

random

variable

lhas the

normal

distribution

N(10,

22)

(c)

Write down

the value

of

(i)

P(r:10)

(ii)

P(r<

10)

(a)

(b)

(1)

a)

(2)

a

)

D-r

s

crr.uh:e--

2n.r

Q-.n

,[r

sta. o-r\.rra

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Kclo)

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t

r)

f(r=

rb\=O

ii)

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to)

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z


3/8

A

large

company

is

analysing

how

much

money

it

spends

on

paper

in its

offices

every

year.

The

number

of

employees,

.tr, and

the

amount

of

money

spent

on

paper,

p

(f

hundreds;,

in

8 randomly

selected

offrces

are

given

in

the

table

below.

x

8

9

t2

t4

7

..,

L6

t9

p (f

hundreds)

40.5

36.1

30.4

39.4

32.6

3

1.1

43.4

45.7

(Youmayuse

I

x2:1160

Lp:299.2

Lpr:11422

Lxp:3449.5)

(a)

Show

that

soo:231.92

and

find

the value

of

s*

and

the

varue

of

%

(b)

calculate

the

product

moment

correlation

coeffrcient

between

x

ar.d,

p.

(2)

The equation

of

the regression

line

ofp

on

x

is given

in the

form

p

:

a -t

bx.

(c)

Show

that,

to 3

significant

figures,

b: 0.824

and

find

the

value

of a.

(4)

(d)

Estimate

the

amount

of

money

spent

on

paper

in

an

office

with

10

employees.

(2)

(e)

Explain

the

effect

each additional

employee

has

on

the

amount

of

money

spent on

paper.

(1)

Later

the

company

realised

it had

made

a

mistake

in

adding

up

its

costs,p.

The

true

costs

were

actually

half

of

the values

recorded.

The product

moment

correlation

coeffrcient

and

the

equation

of

the linear

regression

line

are

recalculated

using

this

information.

(0

Write

down

the

new

value

of

(i)

the

product

moment

correlation

coefficient,

(ii)

the

gradient

of

the regression

line.

(s)

Q)

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5/8

A and

B

are

two

events

such

that

1

P(B):

,

(a)

Find P(A

a B).

2

P(AIB)

=

i

13

PUw B):

-

20

(b)

Draw

a

Venn diagram

to

show

the

events

A, B and all

the associated

probabilities.

Find

(c)

P(A)

(d)

P(B

lr)

(e)

P(A' a

B)

(2)

(3)

(1)

Q)

(1)

-aT(rr,i-B)

;T-


6/8

The

table shows

the

time,

to

the nearest minute,

spent

waiting for

a

taxi by

each

of 80

people

one

Sunday

afternoon.

Waiting

time

(in

minutes)

f,'requency

rfl

24

15

54

9

7

6

8

24

9-10

t4

l1-15

t2

CL^)

0t

3

?-

t

I

2-

5

(f.s

6

7-*

T

?.s

/+

+Y

3

6.rn

R

gv

(a)

Write down

the upper

class

boundary

for

the

24

minute interval.

(1)

A histogram

is

drawn

to

represent

these

data.

The

height

of

the tallest

bar

is

6

cm.

(b)

Calculate the

height

of the second

tallest bar.

(3)

(c)

Estimate

the

number

of

people

with a

waiting time

between

3.5

minutes

and

7 minutes.

(2)

(d)

Use linear interpolation

to

estimate

the

median,

the lower quartile

and

the

upper

quartile

of the

waiting

times.

(4'.)

(e)

Describe

the

skewness

of

these

data,

giving

a

reason

for

your

answer.

(2)

n'=13),{"):

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3.i

q.S

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7/8

The

time

taken,

in

minutes,

by

children

to complete

a

mathematical

ptszzle

is

assumed

to be normally

distributed with

mean

p

and standard

deviation o.

The

puzzle

can be

completed

in less than24

minutes by 80% of

the

children.

For

5Yo of

the children it takes

more

than

28 minutes to complete

the

pruzle.

(a)

Show this

information on the

Normal

curve below.

(2)

(b)

Write

down the

percentage

of

children who

take between 24

minutes and28

minutes

to complete

the

ptnzle.

(1)

(c) (i)

Find two

equations

in

p

and o.

(ii)

Hence

find, to

3 significant

figures, the value

of

p

andthe

value

of

o.

(7)

A

child

is

selected

at random.

(d)

Find the

probability

that the

child

takes

less than

12 minutes

to

complete the

plzzle.

(3)

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8/8

In

a

large

company,

78%

of

employees

are

car

owners,

30%o

of

these

car

owners

are

also

bike

owners,

85%

of

those

who

are

not

car

owners

are

bike

owners.

(a)

Draw

a tree

diagram

to

represent

this information.

(

An

employee

is

selected

at

random.

(b)

Find

the

probability

that

the

employee

is

a

car

owner

or

a bike

owner

but not

both.

(

Another

employee

is

selected

at

random.

Given

that

this

employee

is

a

bike

owner,

(c)

find

the

probability

that

the

employee

is

a

car

owner.

(,

TWo

employees

are

selected

at

random.

(d)

Find

the

probability

that

only

one of

them

is

a bike

owner.

4)

oso-,

I

c

**'

.'.*g

\e,

b)

p(

ce)

+

P(

Bc)

t

O'78y,O

'?O

+

O'

12f O'f,J

s

o+33

.Z

c)

?Gts)

=

P(

c"B)

.ojllg

Pca)

?k)

d)

P(6)

'0'16

Yo')

+

O'LLro

8(

z

o'+zl

?Ccl6)"

oE =O'16

-

O'

tt'zl

Z

O.

qzt

x

o.S+1

x

L

3

c,.

+89

gB'

?

gtb

z

june 2014 (r) ma - s1 edexcel

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