Nathan's Famous restaurants conducts their annual hotdog eating competition every year at Coney Island. Joey "Jaws" Chestnut is the current record holder, having eaten 76 hotdogs and buns in 10 minutes (that's 21,280 calories, just so you know). How does he do it? I treat it like a sport...I tape my practices and figure out how to improve. Let's say that in the population of all humans (i.e. forgetting about Joey for the moment), the mean number of hotdogs eaten in a 10 minute competition is 20 with a standard deviation of 5. The distribution is normal.

Two brave competitors, Julie and Gio, participate in a hotdog eating contest. Their scores are as follows: Julie = 12 hotdogs Gio = 33 hotdogs

1. If we know that another participant in the study eats more hotdogs than 65% of the population, what would his/her corresponding raw score (number of hotdogs)?

2. Based on what you know about the mean and standard deviation of average people, is there any indication that either Julie or Gio seem to fall outside normal range of hotdog quantities in this exciting competition (use a z-score = +/- 2.0 as your cutoff) and may be exhibiting signs of extreme professional hotdog eating skills? What leads you to your claim?

3. Let's say we would like to know what percent of people had eaten a quantity of hotdogs in this competition that falls between that of Julie and Gio. Include a drawn normal distribution with raw scores and z-scores on the x-axis up to 3 standard deviations. Label where Julie and Gio fall on the distribution and shade in the area of interest.