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) =

Community Answer

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