The time to microwave a 50 gram bag of Crunchy Corn popcorn using an automatic setting on a 600W microwave oven has an approximate normal distribution with a mean of 260 seconds and a standard deviation of 15 seconds.

Requirements:

(a) Identify the variable of interest and the unit of measurement of the variable.

(b) The manufacturers of Crunchy Corn want to be as accurate as possible with their labeling. What time should they quote on their packaging such that no more than 10% of their 50 gram bags will take longer than this time to pop, under the stated conditions?

(c) What proportion of 50 gram bags of Crunchy Corn popcorn will take more than 5 minutes to pop under these conditions?