2018 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

(ii)

Let ,

Thus, is minimum when .

(ii)

Note to leave your answers exactly here.

(ii)

(iii)
Required probability

(ii)
is the probability of event B occurring and event A not occurring.

(ii)
Required Probability

(iii)
Required Probability

(iv)

Thus, events and are not independent events.

(v)
Required Probability (3sf)

(ii)
Using GC, (3sf)

The product moment correlation coefficient shows a strong negative linear correlation between the times to run 100 metres and the times to run 10000 metres.

(iii)
Using GC, (2dp)

(iv)
(3sf)

Thus, required time taken is 37.2 minutes.
(v)
Since is within the data range, the estimate is reliable as we are performing interpolation.

Unbiased estimate of population variance

(ii)
Let denote the population mean length of the fish.

Under approximately by Central Limit Theorem, since the sample size is sufficiently large.

We perform a one tailed Z test at 2.5% level of significance.

Using GC,

Since , we reject the scientist’s claim at 2.5% of significance level, and conclude with insufficient evidence that the mean length of fishes is greater than 30 cm.

(iii)
It is not necessary to assume as the sample size of 100 is sufficiently large for us to approximate the sample mean lengths of fishes to a normal distribution.

(iv)

Under approximately by Central Limit Theorem, since the sample size is sufficiently large.

To reject at 10% of significance level,

(round up to 3sf)

Note: round up here to avoid for eg, which will result in non-rejection of claim.

(i)
(3sf)

(ii)

(3sf)

(iii)

(3sf)

(iv)
Let and denote the cost of producing a Type A and Type B components respectively.

(3sf)