Table 3

x

1

2

3

4

5

P(X =x)

0.21

0.197

0.2

0.173

0.22

continue overleaf.../

The researcher is interested in using the information in Table 3 to determine the probability that, from a sample of 10 randomly selected adults, exactly 3 of themexceeds the required standardfor practices towards COFLU-20.

(a) Assist the researcher by:

(i) carefully defining the random variable of interest[1 mark]

(ii) identifying a suitable probability distribution to be used to find the probability that exactly three (3) adults, out of 10, exceeds the required standard for practices towards COFLU-20. State the value(s) of the parameter(s) for this distribution.[3 marks]

(iii) justifying the suitability of the probability distribution identified in part (ii)[4 marks]

(iv) calculating the probability that exactly 3 adults, out of 10, exceeds the required standard for practices against COFLU-20[2 marks]

(b)Individual scores for practices towards COFLU-20 are found to be normally distributed with a mean of 3 and a standard deviation of 1.5 over the entire population. The Ministry of Health wishes to use this information to identify individuals whose score on practices towards COFLU-20 is in the lower 75%, in order to give them relevant information on the best practices towards COFLU-20.You are asked to assist in calculating the score that the Ministry of Health should use to decide whether an individual should be given the relevant information?[5 marks]

Total 15 marks