AQA S1 2010 June — Question 4 14 marks

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2010
SessionJune
Marks14
PaperDownload PDF ↗
TopicBinomial Distribution
TypeProbability of range of values
DifficultyModerate -0.8 This is a straightforward application of binomial distribution with standard cumulative probability calculations. Part (a) requires using tables or calculator for P(X≤10), P(X≥5), and P(6<X<12); part (b) is a single binomial probability calculation; part (c) is a simple expectation calculation using E(X)=np. All parts are routine textbook exercises requiring only direct application of formulas with no problem-solving insight or novel reasoning.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities

4 In a certain country, 15 per cent of the male population is left-handed.
  1. Determine the probability that, in a random sample of 50 males from this country:
    1. at most 10 are left-handed;
    2. at least 5 are left-handed;
    3. more than 6 but fewer than 12 are left-handed.
  2. In the same country, 11 per cent of the female population is left-handed. Calculate the probability that, in a random sample of 35 females from this country, exactly 4 are left-handed.
  3. A sample of 2000 people is selected at random from the population of the country. The proportion of males in the sample is 52 per cent. How many people in the sample would you expect to be left-handed?
    \includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-09_2484_1709_223_153}

4 In a certain country, 15 per cent of the male population is left-handed.
\begin{enumerate}[label=(\alph*)]
\item Determine the probability that, in a random sample of 50 males from this country:
\begin{enumerate}[label=(\roman*)]
\item at most 10 are left-handed;
\item at least 5 are left-handed;
\item more than 6 but fewer than 12 are left-handed.
\end{enumerate}\item In the same country, 11 per cent of the female population is left-handed.

Calculate the probability that, in a random sample of 35 females from this country, exactly 4 are left-handed.
\item A sample of 2000 people is selected at random from the population of the country. The proportion of males in the sample is 52 per cent.

How many people in the sample would you expect to be left-handed?

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-09_2484_1709_223_153}
\end{center}
\end{enumerate}

\hfill \mbox{\textit{AQA S1 2010 Q4 [14]}}