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14 It is known that a hospital has a mean waiting time of 4 hours for its Accident and Emergency (ABE) patients. After some new initiatives were introduced, a random sample of 12 patients from the hOSpital's A&E Department had the following waiting times, in hours. 4.25 3.90 4.15 3.95 4.20 4.15 5.00 3.85 4.25 4.05 3.80 3.95 Carry out a hypothesis test at the 10% signicance level to investigate whether the mean waiting time at this hospital's A&E department has changed. You may assume that the waiting times are normally distributed with standard deviation 0.8 hours. [7 marks] Diedre is a head teacher in a school which provides primary. secondary and sixth-fcn'n education. There are 200 teachers in her school. The number of teachers in each level of education along with their gender is shown in the table below. \"m 9 24 23 35 35 24 (a) A teacher is selected at random. Find the probability that: (a) [i] the teacher is female [1 mark] (a) (ii) the teacher is not a sixthfon'n teacher. [1 mark] i (b) Given that a randomly chosen teacher is male, nd the probability that this teacher is not a primary teacher. [2 marks] (c) Diedre wants to select three different teachers at random to be part of a school project. Calculate the probability that all three chosen are secondary teachers. [2 marks]