Edexcel AS Paper 2 (AS Paper 2) 2022 June

1. The relationship between two variables \(p\) and \(t\) is modelled by the regression line with equation

$$p = 22 - 1.1 t$$ The model is based on observations of the independent variable, \(t\), between 1 and 10

1. Describe the correlation between \(p\) and \(t\) implied by this model. Given that \(p\) is measured in centimetres and \(t\) is measured in days,
2. state the units of the gradient of the regression line. Using the model,
3. calculate the change in \(p\) over a 3-day period. Tisam uses this model to estimate the value of \(p\) when \(t = 19\)
4. Comment, giving a reason, on the reliability of this estimate.

1. A manufacturer of sweets knows that \(8 \%\) of the bags of sugar delivered from supplier \(A\) will be damp.
   A random sample of 35 bags of sugar is taken from supplier \(A\).
   1. Using a suitable model, find the probability that the number of bags of sugar that are damp is
      1. exactly 2
      2. more than 3
   Supplier \(B\) claims that when it supplies bags of sugar, the proportion of bags that are damp is less than \(8 \%\) The manufacturer takes a random sample of 70 bags of sugar from supplier \(B\) and finds that only 2 of the bags are damp.
2. Carry out a suitable test to assess supplier B's claim. You should state your hypotheses clearly and use a \(10 \%\) level of significance.

1. The histogram summarises the heights of 256 seedlings two weeks after they were planted.
   \includegraphics[max width=\textwidth, alt={}, center]{08e3b0b0-2155-4b37-83e3-343c317ca10c-06_1242_1810_287_132}
   1. Use linear interpolation to estimate the median height of the seedlings.
      (4)
   Chris decides to model the frequency density for these 256 seedlings by a curve with equation $$y = k x ( 8 - x ) \quad 0 \leqslant x \leqslant 8$$ where \(k\) is a constant.
2. Find the value of \(k\) Using this model,
3. write down the median height of the seedlings.

1. Jiang is studying the variable Daily Mean Pressure from the large data set.

He drew the following box and whisker plot for these data for one of the months for one location using a linear scale but

• he failed to label all the values on the scale
• he gave an incorrect value for the median
  \includegraphics[max width=\textwidth, alt={}, center]{08e3b0b0-2155-4b37-83e3-343c317ca10c-09_248_1264_573_402}

Daily Mean Pressure (hPa)
Using your knowledge of the large data set, suggest a suitable value for

1. the median,
2. the range.
   (You are not expected to have memorised values from the large data set. The question is simply looking for sensible answers.)
   1. Jiang is studying the variable Daily Mean Pressure from the large data set.
   He drew the following box and whisker plot for these data for one of the months for one nong asing at
   • he gave an incorrect value for the median "
   Using your knowledge of the large data set, suggest a suitable value for
3. the median,
   "
   \includegraphics[max width=\textwidth, alt={}, center]{08e3b0b0-2155-4b37-83e3-343c317ca10c-09_42_31_1213_1304}
   "

5. Manon has two biased spinners, one red and one green. The random variable \(R\) represents the score when the red spinner is spun.
The random variable \(G\) represents the score when the green spinner is spun.
The probability distributions for \(R\) and \(G\) are given below. Manon spins each spinner once and adds the two scores.

1. Find the probability that
   1. the sum of the two scores is 7
   2. the sum of the two scores is less than 4 The random variable \(X = m R + n G\) where \(m\) and \(n\) are integers. $$\mathrm { P } ( X = 20 ) = \frac { 1 } { 6 } \quad \text { and } \quad \mathrm { P } ( X = 50 ) = \frac { 1 } { 4 }$$
2. Find the value of \(m\) and the value of \(n\)