Edexcel AS Paper 2 (AS Paper 2) 2023 June

1. The histogram and its frequency polygon below give information about the weights, in grams, of 50 plums.
   \includegraphics[max width=\textwidth, alt={}, center]{854568d2-b32d-44de-8a9c-26372e509c20-02_908_1307_328_386}
   1. Show that an estimate for the mean weight of the 50 plums is 63.72 grams.
   2. Calculate an estimate for the standard deviation of the 50 plums.
   Later it was discovered that the scales used to weigh the plums were broken.
   Each plum actually weighs 5 grams less than originally thought.
2. State the effect this will have on the estimate of the standard deviation in part (b). Give a reason for your answer.

1. Fred and Nadine are investigating whether there is a linear relationship between Daily Mean Pressure, \(p \mathrm { hPa }\), and Daily Mean Air Temperature, \(t ^ { \circ } \mathrm { C }\), in Beijing using the 2015 data from the large data set.

Fred randomly selects one month from the data set and draws the scatter diagram in Figure 1 using the data from that month. The scale has been left off the horizontal axis. \begin{figure}[h] \end{figure}

1. Describe the correlation shown in Figure 1. Nadine chooses to use all of the data for Beijing from 2015 and draws the scatter diagram in Figure 2. She uses the same scales as Fred. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{854568d2-b32d-44de-8a9c-26372e509c20-04_777_1509_1841_278} \captionsetup{labelformat=empty} \caption{Figure 2}
   \end{figure}
2. Explain, in context, what Nadine can infer about the relationship between \(p\) and \(t\) using the information shown in Figure 2.
3. Using your knowledge of the large data set, state a value of \(p\) for which interpolation can be used with Figure 2 to predict a value of \(t\).
4. Using your knowledge of the large data set, explain why it is not meaningful to look for a linear relationship between Daily Mean Wind Speed (Beaufort Conversion) and Daily Mean Air Temperature in Beijing in 2015.
5. Explain, in context, what Nadine can infer about the relationship between \(p\) and \(t\) using the information shown in Figure 2.

3. In an after-school club, students can choose to take part in Art, Music, both or neither. There are 45 students that attend the after-school club. Of these

• 25 students take part in Art
• 12 students take part in both Art and Music
• the number of students that take part in Music is \(x\)
  1. Find the range of possible values of \(x\)

One of the 45 students is selected at random.
Event \(A\) is the event that the student selected takes part in Art.
Event \(M\) is the event that the student selected takes part in Music.

Determine whether or not it is possible for the events \(A\) and \(M\) to be independent.

1. Past information shows that \(25 \%\) of adults in a large population have a particular allergy.

Rylan believes that the proportion that has the allergy differs from 25\%
He takes a random sample of 50 adults from the population.
Rylan carries out a test of the null hypothesis \(\mathrm { H } _ { 0 } : p = 0.25\) using a \(5 \%\) level of significance.

1. Write down the alternative hypothesis for Rylan's test.
2. Find the critical region for this test. You should state the probability associated with each tail, which should be as close to \(2.5 \%\) as possible.
3. State the actual probability of incorrectly rejecting \(\mathrm { H } _ { 0 }\) for this test. Rylan finds that 10 of the adults in his sample have the allergy.
4. State the conclusion of Rylan's hypothesis test.

1. Julia selects 3 letters at random, one at a time without replacement, from the word

\section*{VARIANCE} The discrete random variable \(X\) represents the number of times she selects a letter A.

1. Find the complete probability distribution of \(X\). Yuki selects 10 letters at random, one at a time with replacement, from the word \section*{DEVIATION}
2. Find the probability that he selects the letter E at least 4 times.