CAIE S1 (Statistics 1) 2018 June

1 Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows. $$\begin{array} { l l l l l l l l l l } 37 & 40 & 45 & 38 & 36 & 38 & 42 & 38 & 40 & 39 \end{array}$$

1. Find the mode.
2. Find the median and the interquartile range.

2 In a group of students, \(\frac { 3 } { 4 }\) are male. The proportion of male students who like their curry hot is \(\frac { 3 } { 5 }\) and the proportion of female students who like their curry hot is \(\frac { 4 } { 5 }\). One student is chosen at random.

1. Find the probability that the student chosen is either female, or likes their curry hot, or is both female and likes their curry hot.
2. Showing your working, determine whether the events 'the student chosen is male' and 'the student chosen likes their curry hot' are independent.

3

1. The volume of soup in Super Soup cartons has a normal distribution with mean \(\mu\) millilitres and standard deviation 9 millilitres. Tests have shown that \(10 \%\) of cartons contain less than 440 millilitres of soup. Find the value of \(\mu\).
2. A food retailer orders 150 Super Soup cartons. Calculate the number of these cartons for which you would expect the volume of soup to be more than 1.8 standard deviations above the mean.

4 Mrs Rupal chooses 3 animals at random from 5 dogs and 2 cats. The random variable \(X\) is the number of cats chosen.

1. Draw up the probability distribution table for \(X\).
2. You are given that \(\mathrm { E } ( X ) = \frac { 6 } { 7 }\). Find the value of \(\operatorname { Var } ( X )\).

5 The lengths, \(t\) minutes, of 242 phone calls made by a family over a period of 1 week are summarised in the frequency table below.

1. Find the value of \(a\).
2. Calculate an estimate of the mean length of these phone calls.
3. On the grid, draw a histogram to illustrate the data in the table.
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6

1. Find the number of ways in which all 9 letters of the word AUSTRALIA can be arranged in each of the following cases.
   1. All the vowels (A, I, U are vowels) are together.
   2. The letter T is in the central position and each end position is occupied by one of the other consonants (R, S, L).
2. Donna has 2 necklaces, 8 rings and 4 bracelets, all different. She chooses 4 pieces of jewellery. How many possible selections can she make if she chooses at least 1 necklace and at least 1 bracelet?

7 In a certain country, \(60 \%\) of mobile phones sold are made by Company \(A , 35 \%\) are made by Company \(B\) and 5\% are made by other companies.

1. Find the probability that, out of a random sample of 13 people who buy a mobile phone, fewer than 11 choose a mobile phone made by Company \(A\).
2. Use a suitable approximation to find the probability that, out of a random sample of 130 people who buy a mobile phone, at least 50 choose a mobile phone made by Company \(B\).
3. A random sample of \(n\) mobile phones sold is chosen. The probability that at least one of these phones is made by Company \(B\) is more than 0.98 . Find the least possible value of \(n\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.