3. {6 marks] {a} Positive attribute soores in a population of high school students have a normal distribution with a mean of 75 and a variance of 225. A random sample of 16 high school students is taken from this population. Show all your workings and round your answer to two decimal places {if it is needed}. {i} what is the probability that a randomly selected student will have score greater than 75? {1 mark} {ii} What is the probability that that a randomly selected student will have score between 65 and 80? {1 mark} {iii} what is the value of the score at the 80th percentile? {1 mark} {h} The likelihood of infection from a needle stick injury in a hospital is under review. A study involving n = 10 workers was conducted and the outcome can be \"infected' or "not infected". The probability of the historical rate of needle stick infection in this hospital is 0.13. Show all your workings and round your answer to two decimal places {if it is needed]. {i} what is the probability of obtaining at least 2 cases of infection? {1 mark] [ii] what is the probability of obtaining less than 2 cases of infection? {1 mark} {iii} If the number of workers n was bigger and the probability of the historical rate of needle stick infection in this hospital was the same 0.13, what effect would that have on the probability of obtaining at least 2 cases of infection? Clearly explain your answer. {1 mark} 4. {4 marks} The American General Social Surveygathers demographic and social data on a small area of US. . A researcher wants to know if there is an association between health insurance coverage and racelethnicity. The researcher obtains the data from the General Social Survey and summarises the results in a cross tabulation. Show all your workings and round your answer to three decimal places {if it is needed}. Health Insurance Racel'Elhnicity Coverage While Black Other YES 10 8 15 NO 9 5 12 a] At the 5% significance level, conduct the hypothesis testing whether there is an association between health insurance coverage and racefethnicity. {3 marks] b] At the 10% significance level, would we expect the p-value to be greater, less than, or equal to .10? State the conclusion relating with the given scenario. Clearly explain your answer. {1 mark]