MEDIUM

AS and A Level

IMPORTANT

Earn 100

A biased coin is tossed $160$ times. The number of heads obtained, $H$ , follows a binomial distribution where $E (H) = 100$ . Find the value of $p$ and the variance of $H$ .

Important Questions on The Normal Distribution

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 6

A biased coin is tossed

160

times. The number of heads obtained,

H

, follows a binomial distribution where

E (H) = 100

. Find the approximate probability of obtaining more than

110

heads.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 7

One card is selected at random from each of

40

packs. Each pack contains

52

cards and includes

13

clubs. Let

C

be the number of clubs selected from the

40

packs. Show that the variance of

C

7.5

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 7

One card is selected at random from each of $40$ packs. Each pack contains $52$ cards and includes $13$ clubs. Let $C$ be the number of clubs selected from the $40$ packs.

Obtain an approximation for the value of $P (C ⩽ 8),$ and justify the use of this approximation.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 8

In a large survey,

55 %

of the people questioned are in full-time employment. In a random sample of

80

of these people, find the expected number in full-time employment.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 8

In a large survey,

55 %

of the people questioned are in full-time employment. In a random sample of

80

of these people, find the standard deviation of the number in full-time employment.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 8

In a large survey,

55 %

of the people questioned are in full-time employment. In a random sample of

80

of these people, find the approximate probability that fewer than half of the sample are in full-time employment.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 9

A company manufactures rubber and plastic washers in the ratio

4 : 1

. The washers are randomly packed into boxes of

25

.
Find the probability that a randomly selected box contains exactly

21

rubber washers.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 8 - The Normal Distribution>EXERCISE 8E>Q 9

A company manufactures rubber and plastic washers in the ratio

4 : 1

. The washers are randomly packed into boxes of

25

.
Find the probability that a randomly selected box contains exactly

10

plastic washers.

A biased coin is tossed 160 times. The number of heads obtained, H, follows a binomial distribution where EH=100. Find the value of p and the variance of H.

Important Questions on The Normal Distribution

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A biased coin is tossed $160$ times. The number of heads obtained, $H$ , follows a binomial distribution where $E (H) = 100$ . Find the value of $p$ and the variance of $H$ .