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My son is a wicketkeeper, and wicketkeepers need gloves. Unfortunately, wicketkeeping gloves wear out over time and need to be replaced. During a typical season, there are 16 games and some games put more wear on a wicketkeeper's gloves than others. Suppose the wear on the inner surface of my son's gloves from each match has a mean of 0.9mm and standard deviation of 0.25mm.
a) If the inner surface of his gloves is 16.5mm thick, what is the approximate chance my son's gloves last out the 16 matches in a season (assuming he plays in all of them)?
b) In fact, wear is uneven between right and left gloves. Suppose wear on the right glove in a match is normal with mean 1mm and standard deviation 0.3mm, while wear on the left glove is normal with mean 0.8mm and standard deviation 0.2mm. Further, suppose the correlation between wear on each glove in the same match is 0.8. If the right glove was worn down by 1.2mm in today's match, what is the probability that today's left glove wear is less than 1mm?
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