Question Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean 𝜇 = 4 ml and standard deviation 𝜎 = 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 following probabilities. (Round your answers to four decimal places.) a - P(x < 4) = .5 b - P(x < 4.2) = .8413 c - P(x ≤ 4.2) = .8413 d - P(3.6 < x < 4.4) = e - P(x > 3.5) = f - P(x > 3) =

GVQCUE The Asker · Probability and Statistics

Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean 𝜇 = 4 ml and standard deviation 𝜎 = 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 following probabilities. (Round your answers to four decimal places.)

a - P(x < 4) = .5
b - P(x < 4.2) = .8413
c - P(x ≤ 4.2) = .8413
d - P(3.6 < x < 4.4) =
e - P(x > 3.5) =
f - P(x > 3) =

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AnswerGiven:-{:[" mear "(mu)=4ml],[" Standard deviation "(sigma)=0.2ml]:}a){:[p(x < 4)=p((x-mu)/(sigma) < (4-4)/(0.2))],[=p(z < 0)],[p(x < 4)=0.5]:}b){:[p(x < 4.2)=p((x-mu)/(sigma) < (4.2-4)/(0.2))],[=p(z < 1)],[p(x < 4.2)=0.8413]:}c){:[p(x <= 4.2)=p((x-mu)/(sigma) <= (4.2-4)/(0.2))],[=p(z <= 1)]:}p(x <= 4.2)=0.8413{:[p(3.6 < x < 4.4)=p((3.6+4)/(0.2) < (x-mu)/(sigma) < (4.4-4)/(0.2))],[=p(-2 < z < 2)]: ... See the full answer