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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.

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