A student is selected at random. Find the probability that the student completes the task in less than $21.8$ minutes.

The probability that a student takes between $k$ and $21.8$ minutes is $0.3$. Find the value of $k$.

Note: There may be slight differences in answers, depending on whether candidates use tables or GDCs, or their 3 sf answers in subsequent parts. Do not penalise answers that are consistent with their working and check carefully for FT.

attempt to standardize     (M1)

eg     $z = \frac{{21.8 - 20}}{{1.25}},{\text{ 1.44}}$

${\text{P}}(T < 21.8) = 0.925$     A1     N2

[2 marks]

Note: There may be slight differences in answers, depending on whether candidates use tables or GDCs, or their 3 sf answers in subsequent parts. Do not penalise answers that are consistent with their working and check carefully for FT.

attempt to subtract probabilities     (M1)

eg     ${\text{P}}(T < 21.8) - {\text{P}}(T < k) = 0.3,{\text{ }}0.925 - 0.3$

${\text{P}}(T < k) = 0.625$     A1

EITHER

finding the $z$-value for $0.625$     (A1)

eg     $z = 0.3186$ (from tables), $z = 0.3188$

attempt to set up equation using their $z$-value     (M1)

eg     $0.3186 = \frac{{k - 20}}{{1.25}},{\text{ }} - 0.524 \times 1.25 = k - 20$

$k = 20.4$     A1     N3

OR

$k = 20.4$     A3     N3

[5 marks]