Weights of four-year-olds are Normally distributed, with a mean of 40 pounds and a standard deviation of 1.3 pounds. At his four-year checkup, Marlon’s weight is measured to be greater than 30% of boys his age. How much does Marlon weigh?

40.7 pounds

Explanation:

Given that:

Mean, m = 40

Standard deviation, σ = 1.3

Weight greater than 30% = 0.3

P(x > Z) = 0.3

Z = (x - m) / σ

P(x > Z) = 0.3

Z = 0.524 ( Z probability calculator)

Hence,

0.524 = (x - 40) / 1.3

0.524 * 1.3 = x - 40

0.6812 = x - 40

x = 0.6812 + 40

x = 40.6812

x = 40.7

Hence, Marlon weighs about 40.7

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