CAIE S1 (Statistics 1) 2019 June

1 Two ordinary fair dice are thrown and the numbers obtained are noted. Event \(S\) is 'The sum of the numbers is even'. Event \(T\) is 'The sum of the numbers is either less than 6 or a multiple of 4 or both'. Showing your working, determine whether the events \(S\) and \(T\) are independent.

2 The volume of ink in a certain type of ink cartridge has a normal distribution with mean 30 ml and standard deviation 1.5 ml . People in an office use a total of 8 cartridges of this ink per month. Find the expected number of cartridges per month that contain less than 28.9 ml of this ink.

3 The probability that Janice will buy an item online in any week is 0.35 . Janice does not buy more than one item online in any week.

1. Find the probability that, in a 10 -week period, Janice buys at most 7 items online.
2. The probability that Janice buys at least one item online in a period of \(n\) weeks is greater than 0.99 . Find the smallest possible value of \(n\).

4 It is known that 20\% of male giant pandas in a certain area weigh more than 121 kg and \(71.9 \%\) weigh more than 102 kg . Weights of male giant pandas in this area have a normal distribution. Find the mean and standard deviation of the weights of male giant pandas in this area.

5 Maryam has 7 sweets in a tin; 6 are toffees and 1 is a chocolate. She chooses one sweet at random and takes it out. Her friend adds 3 chocolates to the tin. Then Maryam takes another sweet at random out of the tin.

1. Draw a fully labelled tree diagram to illustrate this situation.
2. Draw up the probability distribution table for the number of toffees taken.
3. Find the mean number of toffees taken.
4. Find the probability that the first sweet taken is a chocolate, given that the second sweet taken is a toffee.

6

1. Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.
2. The times in minutes taken to run a marathon were recorded for a group of 13 marathon runners and were found to be as follows. $$\begin{array} { l l l l l l l l l l l l l } 180 & 275 & 235 & 242 & 311 & 194 & 246 & 229 & 238 & 768 & 332 & 227 & 228 \end{array}$$ State which of the mean, mode or median is most suitable as a measure of central tendency for these times. Explain why the other measures are less suitable.
3. Another group of 33 people ran the same marathon and their times in minutes were as follows.

   190	203	215	246	249	253	255	254	258	260	261
   263	267	269	274	276	280	288	283	287	294	300
   307	318	327	331	336	345	351	353	360	368	375

   (a) On the grid below, draw a box-and-whisker plot to illustrate the times for these 33 people.
   \includegraphics[max width=\textwidth, alt={}, center]{f4d040a2-6a04-49ce-98ac-8ba5c515f905-09_611_1202_1270_555}
   (b) Find the interquartile range of these times.

7

1. A group of 6 teenagers go boating. There are three boats available. One boat has room for 3 people, one has room for 2 people and one has room for 1 person. Find the number of different ways the group of 6 teenagers can be divided between the three boats.
2. Find the number of different 7-digit numbers which can be formed from the seven digits 2, 2, 3, 7, 7, 7, 8 in each of the following cases.
   1. The odd digits are together and the even digits are together.
   2. The 2 s are not together.
      If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.