statistics
posted by Probability .
A charity believes that when it puts out an appeal for charitable donations the donations it receives will normally distributed with a mean of $50 and standard deviation of $6, and it is assumed that donations will be independent of each other. (i) Find the probability that a sample mean of 5 donations will be smaller than $55. (ii) Find probability that the first donation is at least $3 more than second.

Z = (mean1  mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n1)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores calculated.