CAIE S1 (Statistics 1) 2012 November

1 Ashok has 3 green pens and 7 red pens. His friend Rod takes 3 of these pens at random, without replacement. Draw up a probability distribution table for the number of green pens Rod takes.

2 The amounts of money, \(x\) dollars, that 24 people had in their pockets are summarised by \(\Sigma ( x - 36 ) = - 60\) and \(\Sigma ( x - 36 ) ^ { 2 } = 227.76\). Find \(\Sigma x\) and \(\Sigma x ^ { 2 }\).

3 Lengths of rolls of parcel tape have a normal distribution with mean 75 m , and 15\% of the rolls have lengths less than 73 m .

1. Find the standard deviation of the lengths. Alison buys 8 rolls of parcel tape.
2. Find the probability that fewer than 3 of these rolls have lengths more than 77 m .

4 Prices in dollars of 11 caravans in a showroom are as follows.
\(\begin{array} { l l l l l l l l l l l } 16800 & 18500 & 17700 & 14300 & 15500 & 15300 & 16100 & 16800 & 17300 & 15400 & 16400 \end{array}\)

1. Represent these prices by a stem-and-leaf diagram.
2. Write down the lower quartile of the prices of the caravans in the showroom.
3. 3 different caravans in the showroom are chosen at random and their prices are noted. Find the probability that 2 of these prices are more than the median and 1 is less than the lower quartile.

5 A company set up a display consisting of 20 fireworks. For each firework, the probability that it fails to work is 0.05 , independently of other fireworks.

1. Find the probability that more than 1 firework fails to work. The 20 fireworks cost the company \(
   ) 24\( each. 450 people pay the company \)\\( 10\) each to watch the display. If more than 1 firework fails to work they get their money back.
2. Calculate the expected profit for the company.

6 Ana meets her friends once every day. For each day the probability that she is early is 0.05 and the probability that she is late is 0.75 . Otherwise she is on time.

1. Find the probability that she is on time on fewer than 20 of the next 96 days.
2. If she is early there is a probability of 0.7 that she will eat a banana. If she is late she does not eat a banana. If she is on time there is a probability of 0.4 that she will eat a banana. Given that for one particular meeting with friends she does not eat a banana, find the probability that she is on time.

7

1. In a sweet shop 5 identical packets of toffees, 4 identical packets of fruit gums and 9 identical packets of chocolates are arranged in a line on a shelf. Find the number of different arrangements of the packets that are possible if the packets of chocolates are kept together.
2. Jessica buys 8 different packets of biscuits. She then chooses 4 of these packets.
   1. How many different choices are possible if the order in which Jessica chooses the 4 packets is taken into account? The 8 packets include 1 packet of chocolate biscuits and 1 packet of custard creams.
   2. How many different choices are possible if the order in which Jessica chooses the 4 packets is taken into account and the packet of chocolate biscuits and the packet of custard creams are both chosen?
3. 9 different fruit pies are to be divided between 3 people so that each person gets an odd number of pies. Find the number of ways this can be done.