Edexcel AS Paper 2 (AS Paper 2) 2020 June

1. \begin{figure}[h] \end{figure} The histogram in Figure 1 shows the times taken to complete a crossword by a random sample of students. The number of students who completed the crossword in more than 15 minutes is 78
Estimate the percentage of students who took less than 11 minutes to complete the crossword.

1. Jerry is studying visibility for Camborne using the large data set June 1987.

The table below contains two extracts from the large data set.
It shows the daily maximum relative humidity and the daily mean visibility. (The units for Daily Mean Visibility are deliberately omitted.)
Given that daily mean visibility is given to the nearest 100,

1. write down the range of distances in metres that corresponds to the recorded value 0 for the daily mean visibility. Jerry drew the following scatter diagram, Figure 2, and calculated some statistics using the June 1987 data for Camborne from the large data set. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{d62e5a00-cd23-417f-b244-8b3e24da4aa2-04_823_1764_1281_137} \captionsetup{labelformat=empty} \caption{Figure 2}
   \end{figure} Jerry defines an outlier as a value that is more than 1.5 times the interquartile range above \(Q _ { 3 }\) or more than 1.5 times the interquartile range below \(Q _ { 1 }\).
2. Show that the point circled on the scatter diagram is an outlier for visibility.
3. Interpret the correlation between the daily mean visibility and the daily maximum relative humidity. Jerry drew the following scatter diagram, Figure 3, using the June 1987 data for Camborne from the large data set, but forgot to label the \(x\)-axis.
   \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{d62e5a00-cd23-417f-b244-8b3e24da4aa2-05_730_1056_342_386} \captionsetup{labelformat=empty} \caption{Figure 3}
   \end{figure}
4. Using your knowledge of the large data set, suggest which variable the \(x\)-axis on this scatter diagram represents.

1. In a game, a player can score \(0,1,2,3\) or 4 points each time the game is played.

The random variable \(S\), representing the player's score, has the following probability distribution where \(a , b\) and \(c\) are constants. The probability of scoring less than 2 points is twice the probability of scoring at least 2 points. Each game played is independent of previous games played.
John plays the game twice and adds the two scores together to get a total.
Calculate the probability that the total is 6 points.

1. A lake contains three different types of carp.

There are an estimated 450 mirror carp, 300 leather carp and 850 common carp.
Tim wishes to investigate the health of the fish in the lake.
He decides to take a sample of 160 fish.

1. Give a reason why stratified random sampling cannot be used.
2. Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented. You should state the name of the sampling method used. As part of the health check, Tim weighed the fish.
   His results are given in the table below.

   Weight (wkg)	Frequency (f)	Midpoint (m kg)
   \(2 \leqslant w < 3.5\)	8	2.75
   \(3.5 \leqslant w < 4\)	32	3.75
   \(4 \leqslant w < 4.5\)	64	4.25
   \(4.5 \leqslant w < 5\)	40	4.75
   \(5 \leqslant w < 6\)	16	5.5

   $$\left( \text { You may use } \sum \mathrm { f } m = 692 \quad \text { and } \quad \sum \mathrm { f } m ^ { 2 } = 3053 \right)$$
3. Calculate an estimate for the standard deviation of the weight of the carp. Tim realised that he had transposed the figures for 2 of the weights of the fish.
   He had recorded in the table 2.3 instead of 3.2 and 4.6 instead of 6.4
4. Without calculating a new estimate for the standard deviation, state what effect
   1. using the correct figure of 3.2 instead of 2.3
   2. using the correct figure of 6.4 instead of 4.6
      would have on your estimated standard deviation.
      Give a reason for each of your answers.

1. Afrika works in a call centre.

She assumes that calls are independent and knows, from past experience, that on each sales call that she makes there is a probability of \(\frac { 1 } { 6 }\) that it is successful. Afrika makes 9 sales calls.

1. Calculate the probability that at least 3 of these sales calls will be successful. The probability of Afrika making a successful sales call is the same each day.
   Afrika makes 9 sales calls on each of 5 different days.
2. Calculate the probability that at least 3 of the sales calls will be successful on exactly 1 of these days. Rowan works in the same call centre as Afrika and believes he is a more successful salesperson. To check Rowan’s belief, Afrika monitors the next 35 sales calls Rowan makes and finds that 11 of the sales calls are successful.
3. Stating your hypotheses clearly test, at the \(5 \%\) level of significance, whether or not there is evidence to support Rowan’s belief.