(a)     Tim says he will leave if he is not seated at a table within $25$ minutes of arriving at the restaurant. Find the probability that Tim will leave without being seated.

(b)     Tim has been waiting for $15$ minutes. Find the probability that he will be seated within the next five minutes.

the waiting time, $X{\text{ ~ }}N$($18$, ${4^2}$)

(a)     ${\text{P}}(X > 25) = 0.0401$     (M1)A1

(b)     ${\text{P}}(X < 20|X > 15)$     (A1)

$= \frac{{{\text{P}}(15 < X < 20)}}{{{\text{P}}(X > 15)}}$     (A1)

Note: Only one of the above A1 marks can be implied.

$= \frac{{0.4648...}}{{0.7733...}} = 0.601$     (M1)A1

[6 marks]

Part (a) was well answered, whilst few candidates managed to correctly use conditional probability for part (b).