The number of packages handled by a local courier service is normally distributed. On average 6000 parcels are couriered each day with a standard deviation of 400.

a. Identify the type of distribution being described by the random variable in the problem above and write down the value(s) of its parameter(s).

b. What is the probability the courier service handles more than 7000 parcels on any given day? Also, provide a sentence answering this question.

c. There is a 70% chance the courier service will handle less than a parcels on any given day. Find the number of parcels a.

Also, provide a sentence answering this question.

d. A random sample of 200 days over the past year was selected and the number of parcels couriered recorded. What is the probability the average number of packages couriered was 5920 or fewer? Also, provide a sentence answering this question.