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A factory produces tennis balls whose weights follow a bell-shaped distribution with a mean of 2.06 ounces and a standard deviation of 0.04 ounces. According to the International Tennis Federation (ITF) the mass of an 'official' tennis ball must be in the range of 1.98-2.10 ounces.
a. What proportion of the tennis balls produced by this firm will conform to the weight criterion as defined by the ITF?
b. What proportion of the balls are too small to be used in official tournaments?
c. After recalibrating the machine that produces the tennis balls, the standard deviation has changed (it is not 0.04 ounces anymore), but the mean has remained unchanged (still 2.06 ounces). As a result, the proportion of the balls that are too big (as defined by the ITF) is now 0.025 (25%. What is the value of the new standard deviation?
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