Find the probability when we know the mean and standard deviation for a random sample, as per the central limit theorem. The numerical population of grade point averages at a college has a mean of 2.73 and a standard deviation 0.5. If a random sample of size 110 is taken from the population, what is the probability that the sample mean will be between 2.51 and 2.71?

3. Find the probability of the distribution using the mean x of a random sample of size 65 drawn from a population with a mean of 112 and a standard deviation of 40. Show your work and nd the following; - Find the mean and standard deviation of X. - Find the probability that X assumes a value between 110 and 114. - Find the probability that X assumes a value greater than 113. 4. Find the probability when we know the mean and standard deviation for a random sample, as per the central limit theorem. The numerical population of grade point averages at a college has a mean of 2.73 and a standard deviation 0.5. If a random sample of size 110 is taken from the population, what is the probability that the sample mean will be between 2.51 and 2.71? Show your work and explain your