81 Analysis of bottled water. In a the Scientific American (July 2003) report on whether bottled water is really purified water, the Natural Resources Defense Council found that 25% of bottled-water brands fill their bottles with just tap water. In a random sample of 65 bottled-water brands, let x be the number that contain tap water.

a. Find the mean of x .

b. Find the standard deviation of x .

c. Find the z -score for the value x = 20.

d. Find the approximate probability that 20 or more of the 65 sampled bottled-water brands will contain tap water.