Example for Central Limit Theorem

The average number of  pounds a person consumes in a year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal. Find the probability that a person selected at random consumes less than 224 pounds per year.

X=224

µ=218.4

Ơ=25

z=X-µ =224-218.4 = .22                P(X<224) = P(Z<0.22) =0.0871+0.05

    Ơ             25                                                                                               =0.5871 or 58.71%






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