O SAL MARICO A variable of two populations has a mean of 20 and a standard deviation of 24 for one of the populations and a megan of 20 and a standard deviation of 16 for the other population. Complete parts (a) through (c). ourses . . . se Hom a. For independent samples of size 16 and 4, respectively, find the mean and standard deviation of X, - X2. (Assume that the sampling is done with replacement or that the population is large enough.) signment The mean of X1 - x2 is atCrunch (Type an integer or a decimal. Do not round.) SC Text Conte The standard deviation of x1 - x2 is (Round to four decimal places as needed.) SCO Student Gra b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. scor Study Plan O A. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x1 - x2 to hold . score Video & Res Library O B. No, the variable must be approximately normally distributed on at least one of the two populations for the formulas for the mean and standard deviation of X1 - X2 to hold, as long as the sampling is done with replacement score Additonal M O C. No, the formulas for the mean and standard deviation of X1 - X2 hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough. Accessible Resources O D. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x1 - X2 to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. 2.13% Purchase Of c. Can you conclude that the variable x, - x2 is normally distributed? Explain your answer. RSC Tutor S Next