Purchases made at small “corner stores” were studied by the authors of the paper “Changes in Quantity, Spending, and Nutritional Characteristics of Adult, Adolescent and Child Urban Corner Store Purchases After an Environmental Intervention” (Preventive Medicine [2015]: 81–85). Corner stores were defined as stores that are less than 200 square feet in size, have only one cash register, and primarily sell food. 

After observing a large number of corner store purchases in Philadelphia, the authors reported that the average number of grams of fat in a corner store purchase was 21.1. Suppose that the variable x 5 number of grams of fat in a corner store purchase has a distribution that is approximately normal with a mean of 21.1 grams and a standard deviation of 7 grams.

a. What is the probability that a randomly selected corner store purchase has more than 30 grams of fat?

b. What is the probability that a randomly selected corner store purchase has between 15 and 25 grams of fat?

c. If two corner store purchases are randomly selected, what is the probability that both of these purchases will have more than 25 grams of fat?