After being sprayed with a weedkiller, the survival time of weeds in a field is normally distributed with a mean of 15 days.

(a)     If the probability of survival after 21 days is 0.2 , find the standard deviation of the survival time.

When another field is sprayed, the survival time of weeds is normally distributed with a mean of 18 days.

(b)     If the standard deviation of the survival time is unchanged, find the probability of survival after 21 days.

(a)     required to solve ${\text{P}}\left( {Z < \frac{{21 - 15}}{\sigma }} \right) = 0.8$     (M1)

$\frac{6}{\sigma } = 0.842 \ldots \,\,\,\,\,$(or equivalent)     (M1)

$\Rightarrow \sigma  = 7.13$ (days)     A1     N1

(b)     P(survival after 21 days) = 0.337     (M1)A1

[5 marks]

A straightforward Normal distribution problem, but many candidates confused the z value with the probability.