AQA S1 2006 June — Question 2 12 marks

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2006
SessionJune
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeMultiple probability calculations only
DifficultyModerate -0.8 This is a straightforward application of normal distribution with standard calculations requiring only z-score lookups and basic sampling distribution knowledge. All parts follow routine procedures with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part nature and part (b) requiring understanding of sampling distributions.
Spec2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.01a Permutations and combinations: evaluate probabilities

2 The heights of sunflowers may be assumed to be normally distributed with a mean of 185 cm and a standard deviation of 10 cm .
  1. Determine the probability that the height of a randomly selected sunflower:
    1. is less than 200 cm ;
    2. is more than 175 cm ;
    3. is between 175 cm and 200 cm .
  2. Determine the probability that the mean height of a random sample of 4 sunflowers is more than 190 cm .

2 The heights of sunflowers may be assumed to be normally distributed with a mean of 185 cm and a standard deviation of 10 cm .
\begin{enumerate}[label=(\alph*)]
\item Determine the probability that the height of a randomly selected sunflower:
\begin{enumerate}[label=(\roman*)]
\item is less than 200 cm ;
\item is more than 175 cm ;
\item is between 175 cm and 200 cm .
\end{enumerate}\item Determine the probability that the mean height of a random sample of 4 sunflowers is more than 190 cm .
\end{enumerate}

\hfill \mbox{\textit{AQA S1 2006 Q2 [12]}}