Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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) =

share|improve this question

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

This question appears to be off-topic. The users who voted to close gave these specific reasons:

  • "Homework questions must seek to understand the concepts being taught, not just demand a solution. For help writing a good homework question, see: How to ask a homework question?." – Goos, azimut, TZakrevskiy
  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Lord_Farin, Julian Kuelshammer
If this question can be reworded to fit the rules in the help center, please edit the question.

1 Answer 1

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.

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.