| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Expected profit or cost problem |
| Difficulty | Moderate -0.8 This is a straightforward S1 question testing basic statistical calculations (mean, standard deviation from a frequency table) and simple probability. Part (i) is routine application of formulas with a calculator, and part (ii) involves standard probability calculations with two independent events. The numbers are clean and the methods are textbook standard, making this easier than average for A-level. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.02b Expectation and variance: discrete random variables |
| Prize money | £0 | £10 | £100 | £5000 |
| Frequency | 9929 | 50 | 20 | 1 |
| Answer | Marks |
|---|---|
| (i) | (With ∑ fx= 7500 and ∑ f = 10000 then arriving at the |
| Answer | Marks |
|---|---|
| of 1 slip only after applying the f.t. | B1 for numerical mean |
| Answer | Marks |
|---|---|
| calculator functions | 4 |
| (ii) | P(Two £10 or two £100) |
| Answer | Marks |
|---|---|
| 10000 10000 10000 10000 | M1 for either correct |
| Answer | Marks |
|---|---|
| is also 2.83×10 – 5 | 3 |
| TOTAL | 7 |
Question 7:
--- 7
(i) ---
7
(i) | (With ∑ fx= 7500 and ∑ f = 10000 then arriving at the
mean)
(i) £0.75 scores (B1, B1)
(ii) 75p scores (B1, B1)
(iii) 0.75p scores (B1, B0) (incorrect units)
(iv) £75 scores (B1, B0) (incorrect units)
7500
After B0, B0 then sight of scores SC1. SC1or an answer
10000
in the range £0.74 - £0.76 or 74p – 76p (both inclusive) scores
SC1 (units essential to gain this mark)
Standard Deviation: (CARE NEEDED here with close proximity
of answers)
• 50.2(0) using divisor 9999 scores B2 (50.20148921)
• 50.198 (= 50.2) using divisor 10000 scores B1(rmsd)
• If divisor is not shown (or calc used) and only an answer
of 50.2 (i.e. not coming from 50.198) is seen then award
B2 on b.o.d. (default)
After B0 scored then an attempt at S as evident by either
xx
75002
S = (5000+200000+25000000)− (= 25199375)
xx
10000
or
S = (5000 + 200000 + 25000000) – 10000(0.75)2
xx
scores (M1) or M1ft ‘their 75002’ or ‘their 0.752’
NB The structure must be correct in both above cases with a max
of 1 slip only after applying the f.t. | B1 for numerical mean
(0.75 or 75 seen)
B1dep for correct units
attached
B2 correct s.d.
(B1) correct rmsd
(B2) default
∑ fx2 = 25,205,000
∑x2
Beware =25, 010, 100
After B0 scored then
(M1) or M1f.t. for
attempt at S
xx
NB full marks for correct
results from recommended
method which is use of
calculator functions | 4
(ii) | P(Two £10 or two £100)
50 49 20 19
= × + ×
10000 9999 10000 9999
= 0.0000245 + 0.0000038 = (0.00002450245 + 0.00000380038)
= 0.000028(3) o.e. = (0.00002830283)
50 50 20 20
After M0, M0 then × + × o.e.
10000 10000 10000 10000
Scores SC1 (ignore final answer but SC1 may be implied by
sight of 2.9 ×10 – 5 o.e.)
50 49 20 19
Similarly, × + × scores SC1
10000 10000 10000 10000 | M1 for either correct
product seen
(ignore any multipliers)
M1 sum of both correct
(ignore any multipliers)
A1 CAO (as opposite
with no rounding)
(SC1 case #1)
(SC1 case #2) CARE answer
is also 2.83×10 – 5 | 3
TOTAL | 7A supermarket chain buys a batch of 10000 scratchcard draw tickets for sale in its stores. 50 of these tickets have a £10 prize, 20 of them have a £100 prize, one of them has a £5000 prize and all of the rest have no prize. This information is summarised in the frequency table below.
\begin{tabular}{|c|c|c|c|c|}
\hline
Prize money & £0 & £10 & £100 & £5000 \\
\hline
Frequency & 9929 & 50 & 20 & 1 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Find the mean and standard deviation of the prize money per ticket. [4]
\item I buy two of these tickets at random. Find the probability that I win either two £10 prizes or two £100 prizes. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q7 [7]}}