Question: Manufacturing and Prodcut Development A large part of the luggage market is made up of overnight bags. These bags vary by weight, exterior appearance, material, and size. Suppose the volume of overnight bags is normally distributed with mean μ = 1750 cubic inches and standard deviation σ = 250 cubic inches. A random sample of 15 overnight bags is selected, and the volume of each is found.
a. Find the distribution of X¯.
b. What is the probability that the sample mean volume is more than 1800 cubic inches?
c. What is the probability that the sample mean volume is within 100 cubic inches of 1750?
d. Find a symmetric interval about 1750 such that 95% of all values of the sample mean volume lie in this interval.