Math 1080 HW 5 – Due Monday, March 1 by 11:59 pm BE SURE TO “SHOW YOUR WORK” ON EACH QUESTION !! 1) The birthweights of babies born in Australia in 2019 averaged 3300 grams, with a standard deviation...

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Math 1080 HW 5 – Due Monday, March 1 by 11:59 pm BE SURE TO “SHOW YOUR WORK” ON EACH QUESTION !! 1) The birthweights of babies born in Australia in 2019 averaged 3300 grams, with a standard deviation of 570 grams. The pattern of birthweights was closely approximated by a Normal distribution. Based on these assumptions a) What % of birthweights were greater than 3500 grams ? b) If a random sample of 25 births is chosen, what is the probability the average birthweight from those 25 was greater than 3500 grams ? c) In that random sample of 25 births, there is an 80% chance that the sample mean will be within ___?____ grams of the true population mean of 3300 2) A survey taken by Gallup last November gathered data that suggested the population mean $$ amount that households in a particular metropolitan area planned to spend on “Christmas/holiday” gifts was $850, with a standard deviation of $780. a) We aren’t told the shape of the pattern/distribution of such “household $....” amounts. Could the pattern likely be close to that of a Normal distribution? Explain your reasoning for answering Yes/No. b) If a random sample of 100 households is selected, what is the probability the sample mean from those 100 would be greater than $1000 ? c) You want to select a sample of households from that metro area such that the sample mean has a 98% chance of mis-estimating the population mean by no more than $50. How large a sample will you need to select ?