June 2022 Paper 3 Q3

EdexcelCurrent spec7 marksBinomial Distribution Data Processing Large Data Set

3. Dian uses the large data set to investigate the Daily Total Rainfall, \(r\) mm, for Camborne.

(a) Write down how a value of \(0 \lt r \leqslant 0.05\) is recorded in the large data set. (1)

Dian uses the data for the 31 days of August 2015 for Camborne and calculates the following statistics

\[n = 31 \qquad \sum r = 174.9 \qquad \sum r^2 = 3523.283\]

(b) Use these statistics to calculate

(i) the mean of the Daily Total Rainfall in Camborne for August 2015,

(ii) the standard deviation of the Daily Total Rainfall in Camborne for August 2015. (3)

Dian believes that the mean Daily Total Rainfall in August is less in the South of the UK than in the North of the UK.
The mean Daily Total Rainfall in Leuchars for August 2015 is 1.72 mm to 2 decimal places.

Dian uses the large data set to estimate the proportion of days with no rain in Camborne for 1987 to be 0.27 to 2 decimal places.

(d) Explain why the distribution B(14, 0.27) might not be a reasonable model for the number of days without rain for a 14-day summer event. (1)

Scheme	Marks	AO
tr	B1	1.2
	(1)

Mark scheme (b)

Scheme	Marks	AO
(i) \(\mu = \dfrac{174.9}{31} = 5.6419\ldots\) awrt 5.64	B1	1.1b
(ii) \(\sigma_r = \sqrt{\dfrac{3523.283}{31} - \mu^2}\)	M1	1.1b
\(= 9.04559\ldots\) awrt 9.05	A1	1.1b
	(3)

Notes

(i) B1: For a correct mean awrt 5.64

(ii) M1: For a correct expression for sd including the \(\sqrt{\phantom{x}}\) Ft their mean

A1: awrt 9.05 (Allow \(s = 9.1932\ldots\) awrt 9.19)

NB awrt to 9.05 or 9.19 with no working is M1 A1

Mark scheme (c)

Scheme	Marks	AO
Leuchars is in the North and Camborne is in the South	M1	2.4
The mean is smaller for Leuchars than Camborne therefore there is no evidence that Dian’s belief is true	A1ft	2.2b
	(2)

Notes

M1: For stating Leuchars is North of Camborne oe eg Camborne is further south

A1ft: M1 must be awarded. A correct conclusion and correct comment about the means ft their mean in (b) Allow No

SC: for No and there are only 2 places used so there is insufficient data. Mark as M0A1 on epen

Mark scheme (d)

Scheme	Marks	AO
eg \(p = 0.27\) is unlikely to be constant.	B1	2.4
	(1)
	(7 marks)

Notes

B1: A correct reason referring to

independence (needs context as to what is independent) eg consecutive 14 days unlikely to be independent.
probability [of rain] not being constant.
Allow a comment that conveys the idea that the proportion of days with no rain will be different over the year.