Calculate the range of lifespans of Manx cats whose lifespans are within one standard deviation of the mean.

Estimate the number of Manx cats in a population of 10 000 that will have a lifespan of less than 10 years. Give your answer to the nearest whole number.

\(X \sim N(13.5,{\text{ }}9.5)\)

\(13.5 - \sqrt {9.5}  < X < 13.5 + \sqrt {9.5} \)     (M1)

\(10.4 < X < 16.6\)     A1

Note: Accept 6.16.

[2 marks]

\({\text{P}}(X < 10) = 0.12807 \ldots \)     (M1)(A1)

estimate is 1281 (correct to the nearest whole number).     A1

Note: Accept 1280.

[3 marks]

A large proportion of candidates experienced difficulties with this question. In parts (a) and (b), the most common error was to use σ = 9.5. In part (a), a large number of candidates used their range of values to then unnecessarily find the corresponding probability of that time interval occurring. In part (b), a large number of candidates used an unrealistic lower bound (a large negative value) for time.

A large proportion of candidates experienced difficulties with this question. In parts (a) and (b), the most common error was to use σ = 9.5. In part (a), a large number of candidates used their range of values to then unnecessarily find the corresponding probability of that time interval occurring. In part (b), a large number of candidates used an unrealistic lower bound (a large negative value) for time.