blood cholesterol level of all men age 20-24 follows N(188,41) where the units for the men and standard deviation are in mg/dl. what is the probability that the sample mean takes a value between 185 and 191 if we sample 1000 men

The standard error of the mean of a sample of N is the population standard deviation divided by sqrt(N), so if the second parameter of your N(188, 41) is the population standard deviation, the SEM should be 1.297. So you need to find out how many standard errors each of 185 and 191 are away from the population mean of 188, because the answer you want is the area under a standard Normal curve between them. The first is three units below it, and the second is three units above it - so you want to look up the area to the left of (3/1.297 = 2.314 standard errors) in a set of Normal tables, and subtract from it the area to the left of (-3/1.297 = -2.314 standard errors). I think you'll get 0.99 - 0.01 = 0.98, which ought to be the answer, but do check it.