Briony investigated the variation in daily mean air temperature, x C, for Beijing in May and June 2015. She used the large data set to select a sample of size 15. She selected the first value by generating a random number between 1 and 61 and then selected every fourth value after that. State the sampling technique that Briony used. Briony summarised the data and found, (1) = 15, x = 339.6, 7994.8 b Calculate the standard deviation. An outlier is defined as, 'a data value which is more than two standard deviations from the mean'. (2) c Show that the temperature recorded on 10 May, 9.7 C, is an outlier. (1) d Clean the data and recalculate the mean and standard deviation for the new data set. (3) e From your knowledge of the large data set, explain why Briony's sampling process might not generate a sample of size 15. 2. A ball B moves along a straight line. B is initially at rest at the point O. At time ts, the velocity of B is t(1-2) ms-. Show that the maximum velocity of the ball is- 33 ms 3. A discrete random variable X is modelled using the probability function, P(X = x)=kx, x=1, 2, 3, 4 a Write down, in terms of k, P(X=2). b Find the value of k.