| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability of range of values |
| Difficulty | Standard +0.3 This is a straightforward S2 binomial distribution question requiring standard calculations: part (a) uses binomial tables or calculator for P(5 ≤ X < 11) with clear parameters, and part (b) is a routine one-tailed hypothesis test with explicit significance level. Both parts follow textbook procedures with no conceptual challenges or novel problem-solving required, making it slightly easier than the average A-level question. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion |
| Answer | Marks | Guidance |
|---|---|---|
| 2(a) | notes | |
| X B(30, 0.25) | B1: using B(30, 0.25) | B1 |
| P(X 10) – P(X 4) = 0.8943 – 0.0979 | M1: using P(X 10) – P(X 4) or | |
| P(X > 5) – P(X > 11) oe | M1 A1 | |
| = 0.7964 | A1: awrt 0.796 |
| Answer | Marks |
|---|---|
| (b) | H : p = 0.25 H : p < 0.25 |
| 0 1 | B1: Both hypotheses correct, labelled |
| Answer | Marks | Guidance |
|---|---|---|
| must use p or p(x) or | B1 | |
| B(15, 0.25) | M1: for using B(15, 0.25) | M1 A1 |
| P(X 1) = 0.0802 | A1: awrt 0.0802 or CR X 1 |
| Answer | Marks |
|---|---|
| critical region | M1: A correct statement – do not |
| Answer | Marks |
|---|---|
| tailed test. | dM1 |
| Answer | Marks |
|---|---|
| proportion of houses unable to receive radio | A1: cso (all previous marks awarded) |
Question 2:
--- 2(a) ---
2(a) | notes
X B(30, 0.25) | B1: using B(30, 0.25) | B1
P(X 10) – P(X 4) = 0.8943 – 0.0979 | M1: using P(X 10) – P(X 4) or
P(X > 5) – P(X > 11) oe | M1 A1
= 0.7964 | A1: awrt 0.796
NB a correct answer gains full marks
(b) | H : p = 0.25 H : p < 0.25
0 1 | B1: Both hypotheses correct, labelled
H or NH or H and H or AH or H ,
0 n 1 a
must use p or p(x) or | B1
B(15, 0.25) | M1: for using B(15, 0.25) | M1 A1
P(X 1) = 0.0802 | A1: awrt 0.0802 or CR X 1
(allow P(X 2) = 0.9198)
NB: Allow M1 A1 for a correct CR with no incorrect working
Reject H or Significant or 1 1ies in the
0
critical region | M1: A correct statement – do not
allow contradictory non contextual
statements. Follow through their
Probability/CR (for 1 or 2 tail test). If
no H given then M0. Ignore their
1
comparison. For a probabillity < 0.5,
statement must be correct compared
to 0.1 for 1 tail test and 0.05 for 2
tailed test or if the probability > 0.5,
statement must be correct compared
to 0.9 for 1 tail test and 0.95 for 2
tailed test. | dM1
A1cso
There is evidence that the radio company’s
claim is true.
Or
The new transmitter will reduce the
proportion of houses unable to receive radio | A1: cso (all previous marks awarded)
and a correct statement containing the
word company if writing about the
claim
or radio if full context.
NotesThe proportion of houses in Radville which are unable to receive digital radio is 25\%. In a survey of a random sample of 30 houses taken from Radville, the number, $X$, of houses which are unable to receive digital radio is recorded.
\begin{enumerate}[label=(\alph*)]
\item Find P(5 $\leq X < 11$) [3]
\end{enumerate}
A radio company claims that a new transmitter set up in Radville will reduce the proportion of houses which are unable to receive digital radio. After the new transmitter has been set up, a random sample of 15 houses is taken, of which 1 house is unable to receive digital radio.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Test, at the 10\% level of significance, the radio company's claim. State your hypotheses clearly. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2015 Q2 [8]}}