1. 1
   The number of emails received by 9 employees in one hour is recorded: 3, 7, 5, 3, 9, 3, 6, 5, 7.

   (a)

   What is the median number of emails received?

   [1 mark]

   • A6
   • B5
   • C3
   • D7

   (b)

   What is the mode?

   [1 mark]

   • A3
   • B5
   • C7
   • D6

   (c)

   What is the range?

   [1 mark]

   • A9
   • B3
   • C6
   • D4

   Total for question 1: 3 marks

2. 2
   The cumulative frequency table for the ages, in years, of 50 members of a fitness club is: age $\le 20$: 6; age $\le 30$: 22; age $\le 40$: 38; age $\le 50$: 46; age $\le 60$: 50.

   (a)

   Find an estimate for the median age.

   [2 marks]

   (b)

   Find an estimate for the interquartile range.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A histogram represents the time, in minutes, spent by 150 customers in a shop, grouped into classes: 0\u201310: frequency density 3; 10\u201325: frequency density 4; 25\u201340: frequency density 2; 40\u201360: frequency density 1.5.

   (a)

   Show that the frequencies are consistent with a total of 150 customers, and find the number of customers who spent between 10 and 25 minutes in the shop.

   [3 marks]

   (b)

   Estimate the median time spent in the shop.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In a survey of 60 students, 34 study Geography, 28 study History, and 10 study neither subject.

   (a)

   Find the number of students who study both Geography and History.

   [4 marks]

   (b)

   Find the number of students who study exactly one of the two subjects.

   [4 marks]

   (c)

   A student is selected at random from the 60. Given that the student studies at least one of the two subjects, find the probability that they study both Geography and History.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A bag contains 12 counters: 5 are yellow, 4 are green and 3 are white. A counter is drawn at random.

   (a)

   What is P(the counter is not green)?

   [1 mark]

   • A$\frac{1}{3}$
   • B$\frac{1}{4}$
   • C$\frac{3}{4}$
   • D$\frac{2}{3}$

   (b)

   The counter is drawn, its colour noted, then replaced; this is repeated 120 times. What is the expected number of times a white counter is drawn?

   [1 mark]

   • A30
   • B40
   • C15
   • D36

   (c)

   The events 'drawing a yellow counter' and 'drawing a green counter' are mutually exclusive. What is P(yellow or green)?

   [1 mark]

   • A$\frac{2}{3}$
   • B$\frac{3}{4}$
   • C$\frac{5}{12}$
   • D1

   Total for question 5: 3 marks

6. 6
   The probability that machine A produces a faulty item is 0.05. The probability that machine B produces a faulty item is 0.1. The two machines operate independently, and one item is checked from each machine.

   (a)

   Find the probability that both items are faulty.

   [2 marks]

   (b)

   Find the probability that exactly one of the two items is faulty.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A drawer contains 9 socks: 5 black and 4 white. Two socks are selected at random, one after another, without replacement.

   (a)

   Using a tree-diagram approach, find the probability that both socks are black.

   [3 marks]

   (b)

   Find the probability that the two socks are different colours.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   The baking times, in minutes, for 8 loaves at a bakery are: 18, 25, 12, 30, 22, 15, 28, 20.

   (a)

   Find the mean and the median baking time.

   [4 marks]

   (b)

   A ninth loaf is added with a baking time of 55 minutes. State, with a reason, whether the mean or the median better represents the typical baking time for the 9 loaves.

   [4 marks]

   (c)

   The bakery claims that at least 75% of loaves (using the original 8 baking times) are baked in under 30 minutes. Using the interquartile range of the original 8 baking times, evaluate whether this claim is consistent with the spread of the data.

   [5 marks]

   Total for question 8: 13 marks

End of questions