In july the grass grows 1/2 in a day on a sunny day and 1/4in. a day on a cludy

Question

In july the grass grows 1/2 in a day on a sunny day and 1/4in. a day on a cludy day. In Seattle in july, 75% of the days aresunny and 25% are cloudy. A) determine the expected amount of grassgrowth on a typical day in july. b) determan the expected total grass growth in the month ofjuly. In july the grass grows 1/2 in a day on a sunny day and 1/4in. a day on a cludy day. In Seattle in july, 75% of the days aresunny and 25% are cloudy. A) determine the expected amount of grassgrowth on a typical day in july. b) determan the expected total grass growth in the month ofjuly.

Explanation / Answer

a) The expected amount of grass growth on a typical day can bedetermined by multiplying the amount of sunny/cloudy days by theirrespective probabilities- E(x) = (.75)(.5) + (.25)(.25) = .4375 inches of expected grassgrowth on a typical day b) In order to find the expected total growth for the month ofJuly, simply multiply the amount of days in July (31 days) by theprobability found in (a). E(x) = .4375 * 31 = 13.5625 inches

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