Find the value of \(x\).

In a field experiment, a research team studies a large sample of these birds. The wingspans of each bird are measured correct to the nearest \(0.1\) cm.

Find the probability that a randomly selected bird has a wingspan measured as \(60.2\) cm.

\({\text{P}}(X > x) = 0.99\;\;\;\left( { = {\text{P}}(X < x) = 0.01} \right)\)     (M1)

\( \Rightarrow x = 54.6{\text{ (cm)}}\)     A1

[2 marks]

\({\text{P}}(60.15 \le X \le 60.25)\)     (M1)(A1)

\( = 0.0166\)     A1

[3 marks]

Total [5 marks]

Many candidates did not use the symmetry of the normal curve correctly. Many, for example, calculated the value of \(x\) for which \({\text{P}}(X < x) = 0.99\) rather than \({\text{P}}(X < x) = 0.01\).

Most candidates did not recognize that the required probability interval was \({\text{P}}(60.15 \le X \le 60.25)\). A large number of candidates simply stated that \({\text{P}}(X = 60.2) = 0.166\). Some candidates used \({\text{P}}(60.1 \le X \le 60.3)\) while a number of candidates bizarrely used probability intervals not centred on \(60.2\), for example, \({\text{P}}(60.15 \le X \le 60.24)\).