# Maths Assignment

According to the 2018 LVCVA Report (Las Vegas Visitor Profile Study, 2018): (i) The average cost of a package (hotel/airline, or tour package) was \$921.04 in 2016  and \$910.99 in 2018. Assume the standard deviation of this cost is \$75 for both years. (ii) The average lodging expenditure per night was \$115.15 in 2016, and \$113.66 in 2018. Assume the standard deviation of this cost is \$15 for both years. (iii) Among repeat customers, 48% in 2016 and 40% in 2018 were vising primarily for vacation or pleasure. 1a) What is the probability that a randomly selected visitor coming to Las Vegas on a package tour would have spent between \$890 and \$925 on the tour package in 2018? What assumption are you making in your probability calculation? 1b) What is the probability that the sample mean of 36 randomly selected visitors coming to Las Vegas on a package tour would have spent between \$890 and \$925 on the tour package in 2018? 2) Suppose random samples of 64 visitors each are taken from the 2016 and 2018 populations of visitors. Let xbar be the sample mean cost of the tour package. (a) Find the probability that the difference xbar_2018 – xbar_2016 will be positive. (b) Let phat = sample proportion of repeat visitors coming to Las Vegas primarily for vacation/pleasure. Find the probability that the phat_2018 will be larger than 45%. (c) Find the probability that the phat_2018 – phat_2016 will be > 0.

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