CAIE S1 (Statistics 1) 2014 June

1 The petrol consumption of a certain type of car has a normal distribution with mean 24 kilometres per litre and standard deviation 4.7 kilometres per litre. Find the probability that the petrol consumption of a randomly chosen car of this type is between 21.6 kilometres per litre and 28.7 kilometres per litre.

2 Lengths of a certain type of white radish are normally distributed with mean \(\mu \mathrm { cm }\) and standard deviation \(\sigma \mathrm { cm } .4 \%\) of these radishes are longer than 12 cm and \(32 \%\) are longer than 9 cm . Find \(\mu\) and \(\sigma\).

3

1. State three conditions which must be satisfied for a situation to be modelled by a binomial distribution. George wants to invest some of his monthly salary. He invests a certain amount of this every month for 18 months. For each month there is a probability of 0.25 that he will buy shares in a large company, there is a probability of 0.15 that he will buy shares in a small company and there is a probability of 0.6 that he will invest in a savings account.
2. Find the probability that George will buy shares in a small company in at least 3 of these 18 months.

4 A book club sends 6 paperback and 2 hardback books to Mrs Hunt. She chooses 4 of these books at random to take with her on holiday. The random variable \(X\) represents the number of paperback books she chooses.

1. Show that the probability that she chooses exactly 2 paperback books is \(\frac { 3 } { 14 }\).
2. Draw up the probability distribution table for \(X\).
3. You are given that \(\mathrm { E } ( X ) = 3\). Find \(\operatorname { Var } ( X )\).

5 Playground equipment consists of swings ( \(S\) ), roundabouts ( \(R\) ), climbing frames ( \(C\) ) and play-houses \(( P )\). The numbers of pieces of equipment in each of 3 playgrounds are as follows. Each day Nur takes her child to one of the playgrounds. The probability that she chooses playground \(X\) is \(\frac { 1 } { 4 }\). The probability that she chooses playground \(Y\) is \(\frac { 1 } { 4 }\). The probability that she chooses playground \(Z\) is \(\frac { 1 } { 2 }\). When she arrives at the playground, she chooses one piece of equipment at random.

1. Find the probability that Nur chooses a play-house.
2. Given that Nur chooses a climbing frame, find the probability that she chose playground \(Y\).

6 Find the number of different ways in which all 8 letters of the word TANZANIA can be arranged so that

1. all the letters A are together,
2. the first letter is a consonant ( \(\mathrm { T } , \mathrm { N } , \mathrm { Z }\) ), the second letter is a vowel ( \(\mathrm { A } , \mathrm { I }\) ), the third letter is a consonant, the fourth letter is a vowel, and so on alternately. 4 of the 8 letters of the word TANZANIA are selected. How many possible selections contain
3. exactly 1 N and 1 A ,
4. exactly 1 N ?

7 A typing test is taken by 111 people. The numbers of typing errors they make in the test are summarised in the table below.

1. Draw a histogram on graph paper to represent this information.
2. Calculate an estimate of the mean number of typing errors for these 111 people.
3. State which class contains the lower quartile and which class contains the upper quartile. Hence find the least possible value of the interquartile range.