Question

QUESTION 2

To examine practices towards COFLU-20, the researcher examined the relevant responses from the survey and assigned scores of 1 (below required standard), 2 (poor standards), 3 (satisfactory standards), 4 (meets required standards) and 5 (exceeds required standard) to each respondent. Using X to represent the score for practices against COFLU-20, the probability distribution of X is shown in Table 3 below.

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 them exceeds the required standard for 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

Answer 1

(a) (i) Let X be a random variable representing the number of adults who exceed the required standard for practices towards COFLU-20.

(ii) Then X is a binomial random variable with parameters n and p.  

n=10, p= probability of success= probability of exceeding the required standard for practices towards COFLU-20= 0.22

Then

(iii)

Here we need to find the probability that exactly 3 out of 10 exceed the required standard for practices towards COFLU-20. The probability of exceeding the required standard for practices towards COFLU-20= 0.22

The probability of exceeding the required standard for an adult is independent of another adult. Here total number of adults is 10. So it is similar to the probability of getting exactly 3 successes out of 10 independent trials with probability of success 0.22.

So it is suitable to use Binomial Distribution.

(iv)

(b)

Let X be a random variable representing the  Individual scores for practices towards COFLU-20.

Then X is normally distributed.

Then find x such that

Then

where Z is the standard normal random variable,

We know Pr(Z <=0.674)=0.75

So, So answer is 4.011