CAIE S1 (Statistics 1) 2011 November

1 The following are the times, in minutes, taken by 11 runners to complete a 10 km run.
\(\begin{array} { l l l l l l l l l l l } 48.3 & 55.2 & 59.9 & 67.7 & 60.5 & 75.6 & 62.5 & 57.4 & 53.4 & 49.2 & 64.1 \end{array}\)
Find the mean and standard deviation of these times.

2 Twelve coins are tossed and placed in a line. Each coin can show either a head or a tail.

1. Find the number of different arrangements of heads and tails which can be obtained.
2. Find the number of different arrangements which contain 7 heads and 5 tails.

3

1. Geoff wishes to plant 25 flowers in a flower-bed. He can choose from 15 different geraniums, 10 different roses and 8 different lilies. He wants to have at least 11 geraniums and also to have the same number of roses and lilies. Find the number of different selections of flowers he can make.
2. Find the number of different ways in which the 9 letters of the word GREENGAGE can be arranged if exactly two of the Gs are next to each other.

4 The weights of 220 sausages are summarised in the following table.

1. State which interval the median weight lies in.
2. Find the smallest possible value and the largest possible value for the interquartile range.
3. State how many sausages weighed between 50 g and 60 g .
4. On graph paper, draw a histogram to represent the weights of the sausages.

5 A triangular spinner has one red side, one blue side and one green side. The red side is weighted so that the spinner is four times more likely to land on the red side than on the blue side. The green side is weighted so that the spinner is three times more likely to land on the green side than on the blue side.

1. Show that the probability that the spinner lands on the blue side is \(\frac { 1 } { 8 }\).
2. The spinner is spun 3 times. Find the probability that it lands on a different coloured side each time.
3. The spinner is spun 136 times. Use a suitable approximation to find the probability that it lands on the blue side fewer than 20 times.

6 There are a large number of students in Luttley College. \(60 \%\) of the students are boys. Students can choose exactly one of Games, Drama or Music on Friday afternoons. It is found that \(75 \%\) of the boys choose Games, \(10 \%\) of the boys choose Drama and the remainder of the boys choose Music. Of the girls, \(30 \%\) choose Games, \(55 \%\) choose Drama and the remainder choose Music.

1. 6 boys are chosen at random. Find the probability that fewer than 3 of them choose Music.
2. 5 Drama students are chosen at random. Find the probability that at least 1 of them is a boy.
3. In a certain country, the daily minimum temperature, in \({ } ^ { \circ } \mathrm { C }\), in winter has the distribution \(\mathrm { N } ( 8,24 )\). Find the probability that a randomly chosen winter day in this country has a minimum temperature between \(7 ^ { \circ } \mathrm { C }\) and \(12 ^ { \circ } \mathrm { C }\). The daily minimum temperature, in \({ } ^ { \circ } \mathrm { C }\), in another country in winter has a normal distribution with mean \(\mu\) and standard deviation \(2 \mu\).
4. Find the proportion of winter days on which the minimum temperature is below zero.
5. 70 winter days are chosen at random. Find how many of these would be expected to have a minimum temperature which is more than three times the mean.
6. The probability of the minimum temperature being above \(6 ^ { \circ } \mathrm { C }\) on any winter day is 0.0735 . Find the value of \(\mu\).