Practice Paper 5 (Probability & Statistics 1) (CIE AS Maths: Pure 1)

The Mythical Creatures Research Centre measures the heights, , of nine unicorns to the nearest centimetre. The heights are shown below:

            276       219      198       154        213       243       192       161      218

Find the mean and standard deviation of the nine heights.

A bag contains 12 orange marbles, 8 purple marbles and 5 red marbles. A marble is taken from the bag and its colour is recorded, but it is not replaced in the bag. A second marble is then taken from the bag and its colour is recorded.

Draw a tree diagram to represent this information.

Find the probability that:

The discrete random variable  has the probability distribution shown in the following table:

It is given that 

Show that .

Write down a second equation involving  and .

Hence find the values of and .

Find .

Three letters are chosen at random from the letters in the word REVISION. Find the number of ways that the selection may contain

Write down the number of arrangements of three letters chosen at random from the word REVISION that have exactly one letter I.

Riley is going on holiday and is allowed to bring along four of his toys. At home he has nine different plastic dinosaurs, six different toy cars, and five different wooden reptiles.

How many different selections of his toys can he make if he chooses at least one of each type of toy?

Riley can't decide so he persuades his parents to allow him to bring along five toys instead.

Given that he brings more plastic dinosaurs than any other type of toy, how many different selections can he make now?

A taxi firm, JustDrive, records data on the amount of time, to the nearest minute, that customers had to wait before their taxis arrived.  A random sample of 20 times is given below:

Find the median and interquartile range of the waiting times.

On the grid, draw a box plot for the information given above.

The weight,  kg, of the feed in a sack of pheasant feed produced by a certain manufacturer is modelled as   .

Roger buys twelve sacks of the manufacturer’s pheasant feed to feed to the pheasants who have begun showing up at his backyard bird feeding station.

Find the probability that all twelve sacks contain feed with a weight that is within 35 of 20 .