1. The problem statement, all variables and given/known data You measure the weight of each walnut in a big bag of walnuts and find that the probability distribution of walnut weight is a normal distribution with a mean weight <W> = 30 grams and a standard deviation σW = 5 grams. What is the probability that two randomly chosen walnuts will differ in weight by more than 8 grams? (Hint: find and use the uncertainty in the difference between the measured weights of the two walnuts.) 2. Relevant equations Not entirely sure on this one which to use -- formulas would help greatly if there is one to use in this scenario! I have Z scales with which to assign probabilities to sigma values that I have been using in other portions of the homework. 3. The attempt at a solution I was thinking that the first step here would be to figure out how many standard deviations 8 grams would correspond to, which is 1.6. But the question from there is how to apply this: would the probability be same as a quantity being 1.6 standard deviations away from the mean, or would it be something else? I was thinking that it might be some form of integral inclusive of all sets of points greater than or equal to 1.6 standard deviations apart, but I wasn't sure how to set up this integral. Any help with formulas or the integral would be hugely appreciated!