HARD
AS and A Level
IMPORTANT
Earn 100

At a store, it is known that out of every customers uses a gift voucher in part-payment for purchases. A randomly selected sample of customers is taken. Use a suitable approximation and continuity correction to find the probability that at most of these customers use a gift voucher in part-payment for their purchases.

Important Questions on The Normal Distribution
HARD
AS and A Level
IMPORTANT
A survey shows that of parents believe mathematics to be the most important subject that their children study. Use a suitable approximation to find the probability that at least out of a sample of parents believe mathematics to be the most important subject studied.

MEDIUM
AS and A Level
IMPORTANT
Two normally distributed continuous random variables are and . It is given that and that . On the same diagram, sketch graphs showing the probability density functions of and of . Indicate the line of symmetry of each clearly labelled graph.

HARD
AS and A Level
IMPORTANT
The random variable is such that . A value of is chosen at random and rounded to the nearest whole number. Find the probability that this whole number is .
(Write answer up to decimal places)

HARD
AS and A Level
IMPORTANT
The random variable is such that . Five independent observations of are taken. Find the probability that at most one of them is greater than .
(Write answer up to decimal places)

HARD
AS and A Level
IMPORTANT
The random variable is such that . Find the value of such that .
(Write answer up to decimal places)

MEDIUM
AS and A Level
IMPORTANT
A petrol station finds that its daily sales, in litres, are normally distributed with mean and standard deviation . Find on how many days of the year ( days) the daily sales can be expected to exceed litres.
(Write answer nearest to whole number)

HARD
AS and A Level
IMPORTANT
The daily sales at petrol station are litres, where is normally distributed with mean and standard deviation . It is given that .
Find the value of .
(Round answer up to decimal place)

MEDIUM
AS and A Level
IMPORTANT
The daily sales at petrol station are litres, where is normally distributed with mean and standard deviation . It is given that .
Find the probability that daily sales at this petrol station exceed litres on fewer than of randomly chosen days.
