Probability (Normal population distribution)

[yyh1]

Can anyone help me to solve this question:

A random sample of twenty-five apples is obtained from a normal population distribution with a mean of 80 grams and a standard deviation of 5 grams. Another random sample of 36 apples is obtained from a population distribution having a mean of 75 grams and a standard deviation of 3 grams. Find the probability that the sampling mean from the first sample is bigger than the sampling mean from the second sample with at least 3.4 grams but less than 5.9 grams.

[statdad]

Interesting. What do you know about the sampling distributions of the two means?

[yyh1]

Interesting. What do you know about the sampling distributions of the two means?

Hmm.. no idea.. If u know the answer for this question, kindly explain to me.. thx

[statdad]

the information you need should be in the material you've learned about normal distributions. look in your notes/text for "sampling distribution" or "central limit theorem" - once you have the sampling distribution information, post again.

[yyh1]

I do not get what do u mean by "sampling distribution information", the question is exactly what I written there..

[statdad]

I believe the question is as you posed: it refers to the 'sampling mean' in two locations. That is the quantity to which I referred: if you have this problem to solve, you should have seen something that used that term, or central limit theorem, or sampling distribution.
You need to provide some evidence of working on this before you get help.