In certain hurricane-prone areas of the United States, concrete columns used in construction must meet specific building codes. The minimum diameter for a cylindrical column is 8 inches. Suppose the mean diameter for all columns is 8.25 inches with standard deviation 0.1 inch. A building inspector randomly selects 35 columns and measures the diameter of each.
a. Find the approximate distribution of X . Carefully sketch a graph of the probability density function.
b. What is the probability that the sample mean diameter for the 35 columns will be greater than 8 inches?
c. What is the probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 inches?
d. Suppose the standard deviation is 0.15 inch. Answer parts (a), (b), and (c) using this value of s
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 m = 1750 cubic inches and standard deviation s = 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.