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…/ Page 5 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 (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. (iii) justifying the suitability of the probability distribution identified in part (ii) (iv) calculating the probability that exactly 3 adults, out of 10, exceeds the required standard for practices against COFLU-20 (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 COFLU20 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?
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
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…/
Page 5
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
(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.
(iii) justifying the suitability of the probability distribution identified in part (ii)
(iv) calculating the probability that exactly 3 adults, out of 10, exceeds the required standard
for practices against COFLU-20
(b) Individual scores for practices towards COFLU-20 are found to be
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 COFLU20 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?
(a)
(i)
Random Variable of Interest:
Let us define the random variable X as the number of adults who exceeds the required standard for practices towards COFLU-20.
(ii)
Given that the sample of 10 randomly selected adults and the probability of ‘exceeds the required standard’ is 0.22.
The random variable X follows Binomial distribution with parameters n =10 and p = 0.22.
The probability mass function for the random variable X is,
The probability that exactly three (3) adults, out of 10, exceeds the required standard for practices towards COFLU-20 is,
Requirements for Binomial Distribution:
- The Binomial distribution is useful if the experiment has two outcomes Success and Failure.
- The experiment should have n identical trails.
- The n trails are independent.
- The probability of success is same for every trail.
Checking the requirements:
- Given experiment has two outcomes, ‘exceeds the required standards’ and ‘not exceeds the required standards’.
- Given Experiment is selected 10 adults. That is, the trails are identical.
- Here, the selected 10 adults are independent.
The probability of success (probability) is 0.22 and it is same for every 10 adults
That is, the four requirements for the Binomial distribution are satisfied. Hence, X is a binomial random variable.
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