CAIE S1 (Statistics 1) 2003 June

1

1. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Sales of Superclene Toothpaste} \includegraphics[alt={},max width=\textwidth]{df20f053-8d67-428d-bb19-9447049deed5-2_725_1073_347_497}
   \end{figure} The diagram represents the sales of Superclene toothpaste over the last few years. Give a reason why it is misleading.
2. The following data represent the daily ticket sales at a small theatre during three weeks. $$52,73,34,85,62,79,89,50,45,83,84,91,85,84,87,44,86,41,35,73,86 \text {. }$$ (a) Construct a stem-and-leaf diagram to illustrate the data.
   (b) Use your diagram to find the median of the data.

2 A box contains 10 pens of which 3 are new. A random sample of two pens is taken.

1. Show that the probability of getting exactly one new pen in the sample is \(\frac { 7 } { 15 }\).
2. Construct a probability distribution table for the number of new pens in the sample.
3. Calculate the expected number of new pens in the sample.

3

1. The height of sunflowers follows a normal distribution with mean 112 cm and standard deviation 17.2 cm . Find the probability that the height of a randomly chosen sunflower is greater than 120 cm .
2. When a new fertiliser is used, the height of sunflowers follows a normal distribution with mean 115 cm . Given that \(80 \%\) of the heights are now greater than 103 cm , find the standard deviation.

4 Kamal has 30 hens. The probability that any hen lays an egg on any day is 0.7 . Hens do not lay more than one egg per day, and the days on which a hen lays an egg are independent.

1. Calculate the probability that, on any particular day, Kamal's hens lay exactly 24 eggs.
2. Use a suitable approximation to calculate the probability that Kamal's hens lay fewer than 20 eggs on any particular day.

5 A committee of 5 people is to be chosen from 6 men and 4 women. In how many ways can this be done

1. if there must be 3 men and 2 women on the committee,
2. if there must be more men than women on the committee,
3. if there must be 3 men and 2 women, and one particular woman refuses to be on the committee with one particular man?

6 The people living in 3 houses are classified as children ( \(C\) ), parents ( \(P\) ) or grandparents ( \(G\) ). The numbers living in each house are shown in the table below.

1. All the people in all 3 houses meet for a party. One person at the party is chosen at random. Calculate the probability of choosing a grandparent.
2. A house is chosen at random. Then a person in that house is chosen at random. Using a tree diagram, or otherwise, calculate the probability that the person chosen is a grandparent.
3. Given that the person chosen by the method in part (ii) is a grandparent, calculate the probability that there is also a parent living in the house.

7 A random sample of 97 people who own mobile phones was used to collect data on the amount of time they spent per day on their phones. The results are displayed in the table below.

1. Calculate estimates of the mean and standard deviation of the time spent per day on these mobile phones.
2. On graph paper, draw a fully labelled histogram to represent the data.