Reference no: EM132529339
(a) A researcher selects 20 people at random and records which of three annual-income groups; $0-$20,000, $20,001-$50,000 and more than $50,000 they belong to. Is this situation binomial? Explain in a sentence or two. (1 mark)
(b) A rare disease is reported on average in 2,000 sheep in New Zealand each year. Explain briefly why Poisson distribution would not be appropriate if you were modelling the rare infectious disease that occurred in outbreaks, rather than a rare disease.
(c) A wine company is interested to know the difference in spending for its customers buying red wines compared to clients buying white wines. Average monthly spending, in dollars, on red wines is normally distributed with a mean of 64 and a variance of 6.5 and average monthly spending on white wines is normally distributed with a mean of 52 and a variance of 2.5. Let R be the random variable for average monthly spending on red wines and W be the random variable for average monthly spending on white wines.
(i) What is the expected value of the random variable D, where D = R - W, the difference between average monthly spending on a randomly chosen red wine and a randomly chosen white wine?
(ii) What is the standard deviation of D? (Assume the random variables R and W are independent.)
(iii) Sketch the distribution for D, clearly labelling the important features on your sketch.
(d) A survey of four randomly selected Christchurch sushi stores shows the amount of mercury (in parts per million or ppm) found in Tuna sushi were 0.56, 0.75, 0.10 and 0.95:
(i) What value would be used as the point estimate for the average amount of mercury found in Tuna sushi for Christchurch sushi stores based on this sample? (You do NOT need to work it out.)
(ii) If the standard deviation for the amount of mercury found in Tuna sushi for Christchurch sushi stores is 0.26 and the sample size is 4, calculate the standard error of the sample mean. Show your working including the formula used.
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