Consider the population of all 1-gal cans of dusty rose paint manufactured by a

Question

Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean ? = 4 ml and standard deviation ? = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the probabilities below. (Round all answers to four decimal places.)
(a) P(x < 4) =

(b) P(x < 4.2)=

(c) P(x 4.2) =

(d) P(3.6 < x < 4.2) =

(e) P(x > 3.7) =

(f) P(x > 2.8) =

Explanation / Answer

a) µ = 4 s = 0.2 standardize x to z = (x - µ) / s P(x > 4) = P( z > (4-4) / 0.2) = P(z > 0) = .5 (From Normal probability table) b) µ = 4 s = 0.2 standardize x to z = (x - µ) / s P(x > 4.2) = P( z > (4.2-4) / 0.2) = P(z > 1) = .1587 (From Normal probability table) c) µ = 4 s = 0.2 standardize x to z = (x - µ) / s P( 3.8 -1.5) = .9332 (From Normal probability table)

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