Students are required to answer all 4 questions based on the following Case Scenario The world is currently being adversely affected by the COFLU-20 pandemic. Persons are required to take certain measures to prevent the spread of this virus; however, persons’ knowledge, attitudes and practices towards COFLU-20 may influence their adherence to these measures. A researcher decided to evaluate the knowledge, attitudes and practices towards COFLU-20 of adults living in the English-speaking Caribbean. To gather the data, the researcher developed an online survey consisting of four (4) sections. Section A gathered demographic data on the respondents including their gender, marital status, highest level of education attained, occupation and country of residence. Section B consisted of 15 questions that gathered data on the respondents’ knowledge of COFLU-20. Section C consisted of 10 questions that gathered data on the respondents’ attitudes towards COFLU-20. The final section, Section D, consisted of 5 questions that gathered information on the respondents’ practices against COFLU-20. In order to recruit respondents for this survey, the researcher sent a link to the online survey to persons in his network via email and social media. After receiving 300 responses, the researcher closed down the online survey and deactivated the link to the survey. You are a student pursuing an introductory Statistics course. The researcher has asked that you assist him in summarizing, analyzing and interpreting the information gathered, by answering the questions below. 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 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 (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 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?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Students are required to answer all 4 questions based on the following Case Scenario
The world is currently being adversely affected by the COFLU-20 pandemic. Persons are required to take certain measures to prevent the spread of this virus; however, persons’ knowledge, attitudes and practices towards COFLU-20 may influence their adherence to these measures.
A researcher decided to evaluate the knowledge, attitudes and practices towards COFLU-20 of adults living in the English-speaking Caribbean. To gather the data, the researcher developed an online survey consisting of four (4) sections. Section A gathered demographic data on the respondents including their gender, marital status, highest level of education attained, occupation and country of residence. Section B consisted of 15 questions that gathered data on the respondents’ knowledge of COFLU-20. Section C consisted of 10 questions that gathered data on the respondents’ attitudes towards COFLU-20. The final section, Section D, consisted of 5 questions that gathered information on the respondents’ practices against COFLU-20.
In order to recruit respondents for this survey, the researcher sent a link to the online survey to persons in his network via email and social media. After receiving 300 responses, the researcher closed down the online survey and deactivated the link to the survey.
You are a student pursuing an introductory Statistics course. The researcher has asked that you assist him in summarizing, analyzing and interpreting the information gathered, by answering the questions below.
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 |
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
(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
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