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Q: Consider the population of all one-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ=5 ml and standard deviation σ= .2 ml is a good model for the distribution of the variable x = amount of red dye in the paint mixture. Suppose a one-gallon can of dusty rose paint is randomly selected. Use the normal distribution to calculate the following probabilities.

a. P(x < 5.4) =

b. P(x > 4.7) =

c. P(4.7 < x < 4.9) =

d. P(x < 4.5) =

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closed as off-topic by Lord_Farin, Goos, azimut, Julian Kuelshammer, TZakrevskiy Sep 14 '13 at 12:09

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1 Answer

If $X\sim N(\mu=5, \sigma = 0.2)$, then $\dfrac{X-\mu}{\sigma}=\dfrac{X-5}{0.2}\sim N(0, 1)$. Your first question $P(X< 5.4)= P\left(\dfrac{X-5}{0.2}<\dfrac{5.4-5}{0.2}\right)=P(Z<2)$ where $Z$ is standard normal distributed. You can then go ahead and compute its value.

Similarly you can work on the other three questions.

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