Foundation November 2022 Paper 3 Q16

16 40 students were asked the number of visits they made to a gym one week.

The chart shows information about the results.

(a) Write down the modal number of visits. [1 mark]

(b) Work out the mean number of visits.

Give your answer as a decimal. [3 marks]

Work out the probability that the student visited the gym at least once. [2 marks]

Answer	Mark	Comments
1	B1

Mark scheme (b)

Answer	Mark	Comments
\((0 \times 7\) and\()\) \(1 \times 10\) and \(2 \times 8\) and \(3 \times 7\) and \(4 \times 5\) and \(5 \times 3\) or (0 and) 10 and 16 and 21 and 20 and 15 or 82	M1	allow one error or omission
\(\dfrac{(0 +)\, 10 + 16 + 21 + 20 + 15}{40}\) or \(82 \div 40\) or their \(82 \div 40\)	M1dep	oe eg \(\dfrac{82}{40}\) or \(\dfrac{41}{20}\) or \(2\dfrac{1}{20}\)
2.05	A1	accept 2.1 or 2 with \(82 \div 40\) seen

\(82 \div 6\) or \(82 \div 15\)	M1M0
\(0 \times 7 + 1 \times 10 + 2 \times 8 + 3 \times 7 + 4 \times 5 + 5 \times 2\) (\(5 \times 2\) is one error) \(77 \div 40 = 1.925\)	M1M1A0
\(7 + 10 + 16 + 21 + 20 + 15\) (7 is one error) \(89 \div 40 = 2.225\)	M1M1A0
\(10 + 21 + 20 + 15\) (16 missing is one omission) \(66 \div 40 = 1.65\)	M1M1A0
\((0 +)\; 10 + 16 + 21 + 20 + 15 \div 40\) with missing brackets not recovered	M1M0
Correct products or values seen but a different method used is a choice of methods eg (0) 10 16 21 20 15 followed by \(40 \div 6\) or \(40 \div 15\)	M0

Mark scheme (c)

Answer	Mark	Comments
\(10 + 8 + 7 + 5 + 3\) or 33 or \(40 - 7\) or 33 or \(\dfrac{7}{40}\)	M1	oe
\(\dfrac{33}{40}\) or 0.825 or 82.5%	A1	oe accept 0.83 or 83%

M1 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts
Ignore conversion attempt after correct answer seen
33 out of 40	M1A0
33 : 40	M1A0

1 with 10 indicated as the greatest frequency eg 1 scores 10	B1
1 (10)	B0
1, 10 is the most	B0
1 and 10	B0