CAIE S1 (Statistics 1) 2015 June

1 The weights, in grams, of onions in a supermarket have a normal distribution with mean \(\mu\) and standard deviation 22. The probability that a randomly chosen onion weighs more than 195 grams is 0.128 . Find the value of \(\mu\).

2 When Joanna cooks, the probability that the meal is served on time is \(\frac { 1 } { 5 }\). The probability that the kitchen is left in a mess is \(\frac { 3 } { 5 }\). The probability that the meal is not served on time and the kitchen is not left in a mess is \(\frac { 3 } { 10 }\). Some of this information is shown in the following table.

1. Copy and complete the table.
2. Given that the kitchen is left in a mess, find the probability that the meal is not served on time.

3 On a production line making cameras, the probability of a randomly chosen camera being substandard is 0.072 . A random sample of 300 cameras is checked. Find the probability that there are fewer than 18 cameras which are substandard.

4 A pet shop has 9 rabbits for sale, 6 of which are white. A random sample of two rabbits is chosen without replacement.

1. Show that the probability that exactly one of the two rabbits in the sample is white is \(\frac { 1 } { 2 }\).
2. Construct the probability distribution table for the number of white rabbits in the sample.
3. Find the expected value of the number of white rabbits in the sample.

5 The heights of books in a library, in cm, have a normal distribution with mean 21.7 and standard deviation 6.5. A book with a height of more than 29 cm is classified as 'large'.

1. Find the probability that, of 8 books chosen at random, fewer than 2 books are classified as large.
2. \(n\) books are chosen at random. The probability of there being at least 1 large book is more than 0.98 . Find the least possible value of \(n\).

6 Seventy samples of fertiliser were collected and the nitrogen content was measured for each sample. The cumulative frequency distribution is shown in the table below.

1. On graph paper draw a cumulative frequency graph to represent the data.
2. Estimate the percentage of samples with a nitrogen content greater than 4.4.
3. Estimate the median.
4. Construct the frequency table for these results and draw a histogram on graph paper.

7 Rachel has 3 types of ornament. She has 6 different wooden animals, 4 different sea-shells and 3 different pottery ducks.

1. She lets her daughter Cherry choose 5 ornaments to play with. Cherry chooses at least 1 of each type of ornament. How many different selections can Cherry make? Rachel displays 10 of the 13 ornaments in a row on her window-sill. Find the number of different arrangements that are possible if
2. she has a duck at each end of the row and no ducks anywhere else,
3. she has a duck at each end of the row and wooden animals and sea-shells are placed alternately in the positions in between.