HARD
AS and A Level
IMPORTANT
Earn 100

At a store, it is known that 1 out of every 9 customers uses a gift voucher in part-payment for purchases. A randomly selected sample of 72 customers is taken. Use a suitable approximation and continuity correction to find the probability that at most 6 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 54% 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 30 out of a sample of 50 parents believe mathematics to be the most important subject studied.
MEDIUM
AS and A Level
IMPORTANT
Two normally distributed continuous random variables are X and Y. It is given that X~N1.5, 0.22 and that Y~N2.0, 0.52. On the same diagram, sketch graphs showing the probability density functions of X and of Y. Indicate the line of symmetry of each clearly labelled graph.
HARD
AS and A Level
IMPORTANT

The random variable X is such that X~N82, 126. A value of X is chosen at random and rounded to the nearest whole number. Find the probability that this whole number is 84.

(Write answer up to 3 decimal places)

HARD
AS and A Level
IMPORTANT

The random variable X is such that X~N82, 126. Five independent observations of X are taken. Find the probability that at most one of them is greater than 87.

(Write answer up to 3 decimal places)

HARD
AS and A Level
IMPORTANT
The random variable X is such that X~N82, 126. Find the value of k such that P87<X<k=0.3.

(Write answer up to 3 decimal places)

MEDIUM
AS and A Level
IMPORTANT
A petrol station finds that its daily sales, in litres, are normally distributed with mean 4520 and standard deviation 560. Find on how many days of the year (365 days) the daily sales can be expected to exceed 3900 litres.

(Write answer nearest to whole number)

HARD
AS and A Level
IMPORTANT

The daily sales at petrol station are X litres, where X is normally distributed with mean m and standard deviation 560. It is given that PX>8000=0.122.

Find the value of m.

(Round answer up to 1 decimal place)

MEDIUM
AS and A Level
IMPORTANT
The daily sales at petrol station are X litres, where X is normally distributed with mean m and standard deviation 560. It is given that PX>8000=0.122.

Find the probability that daily sales at this petrol station exceed 8000 litres on fewer than 2 of 6 randomly chosen days.