Edexcel AS Paper 2 (AS Paper 2) 2024 June

1. A coach recorded the heights of some adult rugby players and found the following summary statistics.

$$\begin{array} { r } \text { Median } = 1.85 \mathrm {~m}
\text { Range } = 0.28 \mathrm {~m}
\text { Interquartile range } = 0.11 \mathrm {~m} \end{array}$$ The coach also noticed that

• the height of the shortest player is 1.72 m
• \(25 \%\) of the players' heights are below the height of a player whose height is 1.81 m

Draw a box and whisker plot to represent this information on the grid below.
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1. Keith is studying the variable Daily Mean Wind Direction, in degrees, from the large data set.

Keith summarised the data for Camborne from 1987 into 4 directions \(A , B , C\) and \(D\) representing North, South, East and West in some order.

1. Using your knowledge of the large data set state, giving a reason, which direction \(A\) represents. The entry for Hurn on 27th September 1987 was 999
2. State, giving a reason, what Keith should do with this value.

1. Customers in a shop have to queue to pay.

The partially completed table below and partially completed histogram opposite, give information about the time, \(x\) minutes, spent in the queue by each of 112 customers one day. No customer spent less than 1 minute or longer than 8 minutes in the queue.

1. Complete the table.
2. Complete the histogram. Ting decides to model the frequency density for these 112 customers by a curve with equation $$y = \frac { k } { x ^ { 2 } } \quad 1 \leqslant x \leqslant 8$$ where \(k\) is a constant.
3. Find the value of \(k\)
   \includegraphics[max width=\textwidth, alt={}]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-07_1584_1189_285_443}
   Only use this grid if you need to redraw your histogram.
   \includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-09_1582_1192_367_440}
   \includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-09_2267_51_307_36}

4. The random variable \(X \sim \mathrm {~B} ( 27,0.35 )\)

1. Find
   1. \(\mathrm { P } ( X = 10 )\)
   2. \(\mathrm { P } ( 12 \leqslant X < 15 )\) Historical records show that the proportion of defective items produced by a machine is 0.12 Following a maintenance service of the machine, a random sample of 60 items is taken and 3 defective items are found.
2. Carry out a suitable test to determine whether the proportion of defective items produced by the machine has decreased following the maintenance service. You should state your hypotheses clearly and use a \(5 \%\) level of significance.
3. Write down the \(p\)-value for your test in part (b)

1. A biased 4 -sided spinner has the numbers \(6,7,8\) and 10 on it.

The discrete random variable \(X\) represents the score when the spinner is spun once and has the following probability distribution, where \(q\) is a probability.

1. Find the value of \(q\) Karen spins the spinner repeatedly until she either gets a 7 or she has taken 4 spins.
2. Show that the probability that Karen stops after taking her 3rd spin is 0.128 The random variable \(S\) represents the number of spins Karen takes.
3. Find the probability distribution for \(S\) The random variable \(N\) represents the number of times Karen gets a 7
4. Find \(\mathrm { P } ( S > N )\)