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A firm of caterers wishes to buy fruit juice for a wedding reception of 220 guests. They estimate that on an average, each guest will drink 45 cl of juice. The volume of juice in the bottles they buy may be assumed to have a distribution with mean 70.5 cl and the standard deviation 1.2 cl. Show that if they buy 128 bottles then the caterers can be more than 95% certain that their requirements will be met.