A recent article published using data from Tunisian dairy herds provided this information on milk productivity for an individual dairy cow:

Item:(Milk,kg/cow/year) :4500 :850 Minimum:1900 Maximum: 7500

The study noted that annual milk production per cow follows a normal distribution.

a.What is the amount of milk produced by a cow at the 16th percentile of the distribution of milk from all Tunisian cows?

b.What is the amount of milk produced by a cow just at the third quartile of milk production? [Hint: Are you going from a known value of y to a percentage in the distribution? Or from a known percentage in the distribution to an unknown value of y? ] Should your thinking on graph b.

c.What are the lower and upper values of milk production that would be associated with the middle 50 percent of the distribution?

d. Bagra is a wildly popular mobile cellphone game. The game involves trying to steal cows from other competitors, while keeping your herd intact. A few years ago, the BBC reported from Tunisia about a Tunisian couple who had triumphed at the game and were rewarded with Pamela the cow. (see picture and video) After a few months, the couple claimed Pamela was producing a whopping 6,500 kg. of milk per year. What percentage of Tunisian cows produce more milk than Pamela? Show your thinking on Graph d. (Either show the part of the distribution you know, or show the part you would like to identify).

Graph b. Graph d. Z Z y (kg milk) y (kg milk) Graph b. Graph d. Z Z y (kg milk) y (kg milk)