# Homework Help: Probablility of 2 means

1. Nov 27, 2017

### tzx9633

1. The problem statement, all variables and given/known data
Two independent experiments are being run in which two different types of paints are compared. Eighteen specimens are painted using type A and the drying time in hours is recorded on each. The same is done with type B. The population standard deviations are both known to be 1.0.

Assuming that the mean drying time is equal for the two types of paint, find P(XA–XB>0.3), where XA and XB are the average drying times for samples of size nA = nB = 20. XA and XB has the same mean.

2. Relevant equations

3. The attempt at a solution
σ between 2 means = sqrt ( 2x(1/sqrt(20))^2 ) = 0.316

P(XA–XB>0.3) = P ( z > ( 0.3 - 0) / 0.316) = 0.171 , but the an sprovided is 0.00135 , is my ans wrong ?

2. Nov 27, 2017

### Orodruin

Staff Emeritus
XA-XB is a sum of 36 stochastic variables. What is the distribution of XA-XB and how do you reach that conclusion?

Edit: Actually your question is unclear. It states eighteen samples for each paint but then jumps to nA = nB = 20. Which is it?

3. Nov 27, 2017

### tzx9633

so
sorry , typo there . n1 = n2 = 20 , so XA-XB = (0, 0.316)

4. Nov 27, 2017

### Orodruin

Staff Emeritus
It is not so important what you call them as much as what they are. What I am asking about is the apparent discrepancy between
and

5. Nov 27, 2017

### tzx9633

ignore the 18 , take n1 = n2 = 20

6. Nov 27, 2017

### Ray Vickson

7. Nov 28, 2017

### WWGD

I would suggest, tzx, more a matter of taste, I guess, you mention at least slightly your use of the CLT here.

8. Nov 28, 2017

### Orodruin

Staff Emeritus
I second this. There is no mention of the drying times having a normal distribution so it is an important point.

Edit: Along the same lines, giving the answer with three significant digits is probably quoting a bit more precision than available.

9. Nov 28, 2017

### WWGD

Together with the assumed independence, to avoid covariance issues, and maybe some reference to adding i.i.d RVs..