Gerhard walks to school each morning. The probability that he arrives late is 0.15 and is independent of whether he arrives late on any other morning.
b) The following table summarises the number of late arrivals of all pupils who attended Gerhard's school on five mornings of a practical week.
Number of late arrivals: 0, Number of pupils: 275
Number of late arrivals: 1, Number of pupils: 111
Number of late arrivals: 2, Number of pupils: 33
Number of late arrivals: 3, Number of pupils 12
Number of late arrivals: 4, Number of pupils 13
Number of late arrivals: 5, Number of pupils: 16
(That table is meant to be 2 columns, one for late arrivals and one for corresponding number of pupils)
i) Calculate the mean and the standard deviation of the data in the table.
ii) Show that for the pupils represented in the table, an estimate of the probability of a pupil arriving late on a particular morning is 0.15.
