Lorraine computed a confidence interval for μ based on a sample of size 41. since she did not know σ, she used s in her calculations. lorraine used the normal distribution for the confidence interval instead of a student's t distribution. will her interval be longer or shorter than one obtained by using an appropriate student's t distribution? explain. shorter. for d. f. = 40, zc is greater than tc. shorter. for d. f. = 40, zc is less than tc. longer. for d. f. = 40, zc is less than tc. longer. for d. f. = 40, zc is greater than tc.