CAIE S1 (Statistics 1) 2015 June

1 The lengths, in metres, of cars in a city are normally distributed with mean \(\mu\) and standard deviation 0.714 . The probability that a randomly chosen car has a length more than 3.2 metres and less than \(\mu\) metres is 0.475 . Find \(\mu\).

2 The table summarises the lengths in centimetres of 104 dragonflies.

1. State which class contains the upper quartile.
2. Draw a histogram, on graph paper, to represent the data.

3 Jason throws two fair dice, each with faces numbered 1 to 6 . Event \(A\) is 'one of the numbers obtained is divisible by 3 and the other number is not divisible by 3 '. Event \(B\) is 'the product of the two numbers obtained is even'.

1. Determine whether events \(A\) and \(B\) are independent, showing your working.
2. Are events \(A\) and \(B\) mutually exclusive? Justify your answer.

4
\includegraphics[max width=\textwidth, alt={}, center]{c0c7e038-805a-4237-a579-a6571b84f337-2_451_1530_1393_303} A survey is undertaken to investigate how many photos people take on a one-week holiday and also how many times they view past photos. For a randomly chosen person, the probability of taking fewer than 100 photos is \(x\). The probability that these people view past photos at least 3 times is 0.76 . For those who take at least 100 photos, the probability that they view past photos fewer than 3 times is 0.90 . This information is shown in the tree diagram. The probability that a randomly chosen person views past photos fewer than 3 times is 0.801 .

1. Find \(x\).
2. Given that a person views past photos at least 3 times, find the probability that this person takes at least 100 photos.

5 The table shows the mean and standard deviation of the weights of some turkeys and geese.

1. Find the mean weight of the 27 birds.
2. The weights of individual turkeys are denoted by \(x _ { t } \mathrm {~kg}\) and the weights of individual geese by \(x _ { g } \mathrm {~kg}\). By first finding \(\Sigma x _ { t } ^ { 2 }\) and \(\Sigma x _ { g } ^ { 2 }\), find the standard deviation of the weights of all 27 birds.

6

1. In a certain country, \(68 \%\) of households have a printer. Find the probability that, in a random sample of 8 households, 5, 6 or 7 households have a printer.
2. Use an approximation to find the probability that, in a random sample of 500 households, more than 337 households have a printer.
3. Justify your use of the approximation in part (ii).

7

1. Find how many different numbers can be made by arranging all nine digits of the number 223677888 if
   1. there are no restrictions,
   2. the number made is an even number.
2. Sandra wishes to buy some applications (apps) for her smartphone but she only has enough money for 5 apps in total. There are 3 train apps, 6 social network apps and 14 games apps available. Sandra wants to have at least 1 of each type of app. Find the number of different possible selections of 5 apps that Sandra can choose.