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5. (a) The masses of postgraduate students in a certain country in Africa were found to be normally distributed with a mean of 68kg and a standard deviation of 10kg. Find the probability thatthe mass of a randomly selected postgraduate student in the mentioned country (i) ls less than 78 kg [4] (ii) ls greater than 70 kg [5] (iii) Lies between 60kg and 76kg. [8] (iv) Give any three characteristics of the normal distribution [3] (b) An Educational Psychology student wanted to establish if there is an association between learners' anxiety levels and degrees of irrational thinking. After collecting data using anxiety and irrational belief scales from 10 learners, the student obtained the following outcomes shown in Table 5.1: Table 5.1 Learner A B C D E G H I J Anxiety score (x) 70 48 67 90 85 64 68 55 30 88 Irrationality score (y) 76 43 57 87 78 66 67 52 37 82 (ii) Calculate Pearson's product moment correlation coefficient and comment on it. [35] (iii) Find the coefficient of determination and comment on it. [5] (d) A Psychology of Education lecturer claimed that university students' attitudes towards Research Methods and Statistics were dependent on gender. In an attempt to verify the claim, data was collected and the outcomes were as shown below: Attitudes towards Research Methods and Gender Statistics Positive Neutral Negative Female 38 14 18 Male 32 37 17 Showing all the necessary steps, carry out a chi-square test at the 5% significance level to determine if there is an association between students' gender and their attitudes towards Research Methods and Statistics. [40]