EASY
AS and A Level
IMPORTANT
Earn 100

Describe the binomial distribution that can be approximated by the normal distribution N14, 10.5

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 4
By first evaluating np and npq, use a suitable approximation and continuity correction to find PX<75 for the discrete random variable X~B100, 0.7.
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 5
The discrete random variable Y~B50, 0.6. Use a suitable approximation and continuity correction to find PY>26.
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 EH=100. Find the value of p and the variance of H.
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 EH=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 is 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 PC⩽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.