Basic Probability: WJEC GCSE Higher November 2016 Unit 2 Q7

Higher November 2016 Unit 2 Q7

WJECHigherCurrent spec4 marksBasic Probability

7. A factory uses a machine to produce electrical sockets.
The manager carries out a survey to investigate the probability of the machine producing a defective socket.

The relative frequency of defective sockets produced was calculated after testing a total of 1000, 2000, 3000, 4000 and 5000 sockets.
The results are plotted on the graph below.

Graph of relative frequency of defective sockets (0 to 0.08) against number of sockets tested (0 to 5000); plotted points joined by dashed lines at 1000: 0.03, 2000: 0.042, 3000: 0.05, 4000: 0.046, 5000: 0.048

(a) How many of the first 3000 sockets tested were defective? [2]

(b) Write down the best estimate for the probability that one socket, selected at random, will be defective.
You must give a reason for your choice. [2]

Probability: ……………………

Reason: …………………………………………

Mark scheme (a)

Scheme	Marks	Comments
3000 × 0·05 or equivalent.	M1	Allow 5% of 3000 for the M1.
= 150	A1	C.A.O. SC1 for sight of 3000 × 0·05 (= 150) within an incorrect solution. e.g. 1000 × 0·03 + 2000 × 0·042 + 3000 × 0·05 +… (= 30 + 84 + 150 + …..)

Mark scheme (b)

Scheme	Marks	Comments
0·048 or equivalent e.g. 4·8% or 240/5000	B1	ISW from an answer given as a fraction.
Explanation e.g. ‘all data used’, ‘last point plotted’, ‘the number of sockets tested was the highest’.	B1	Accept any indication that the final reading should give the best estimate.