Evaluate claims about large data set

1. Ming is studying the large data set for Perth in 2015

He intended to use all the data available to find summary statistics for the Daily Mean Air Temperature, \(x { } ^ { \circ } \mathrm { C }\).
Unfortunately, Ming selected an incorrect variable on the spreadsheet.
This incorrect variable gave a mean of 5.3 and a standard deviation of 12.4

1. Using your knowledge of the large data set, suggest which variable Ming selected. The correct values for the Daily Mean Air Temperature are summarised as $$n = 184 \quad \sum x = 2801.2 \quad \sum x ^ { 2 } = 44695.4$$
2. Calculate the mean and standard deviation for these data. One of the months from the large data set for Perth in 2015 has
   • mean \(\bar { X } = 19.4\)
   • standard deviation \(\sigma _ { x } = 2.83\)
     for Daily Mean Air Temperature.
   • Suggest, giving a reason, a month these data may have come from.

13 A reporter is writing an article on the \(\mathrm { CO } _ { 2 }\) emissions from vehicles using the Large Data Set. The reporter claims that the Large Data Set shows that the CO2 emissions from all vehicles in the UK have declined every year from 2002 to 2016. Using your knowledge of the Large Data Set, give two reasons why this claim is invalid.
[0pt] [2 marks]
\includegraphics[max width=\textwidth, alt={}, center]{6ad3bac9-bf08-443d-8be2-b0c26209ffe8-19_2488_1716_219_153} \begin{center} \begin{tabular}{|l|l|l|} \hline 14 & 14 (b) (ii) Find \(\mathrm { P } ( X < 4 )\) \(\text { Find } \mathrm { P } ( X < 4 )\) [2 marks] \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) & \begin{tabular}{l} A customer service centre records every call they receive.
It is found that \(30 \%\) of all calls made to this centre are complaints.
A sample of 20 calls is selected.
The number of calls in the sample which are complaints is denoted by the random variable \(X\).
State two assumptions necessary for \(X\) to be modelled by a binomial distribution.