use R

Normal distribution

Suppose that visitors at a theme park spend an average of $100 on souvenirs. Assume that the money spent is normally distributed with a standard deviation of $10.

a) Plot the PDF of this distribution covering the three standard deviations on either side of the mean. b) What are the chances that a randomly selected visitor will spend more than $120? c) What is the chance that a randomly selected visitor will spend between $80 and $90 (inclusive)?

d) What are the chances of spending within one standard deviation, two standard deviations, and three standard deviations, respectively? e) Between what two values will the middle 80% of the money spent will fall? f) If the theme park gives a free T-shirt for the top 2% of the spenders, what will be the minimum amount you have to spend to get the free T-shirt?

g) Show a plot for 10,000 visitors using the above distribution.