A variable of two populations has a mean of 45 and a standard deviation of 16 for one of the populations and a mean of 45 and a standard deviation of 9 for the other population. Complete parts (a) through (c). a. For independent samples of size 16 and 9, respectively, nd the mean and standard deviation of i1 -)_(2. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of i1 )_(2 is (Type an integer or a decimal, Do not round.) The standard deviation of i1 - i2 is . (Round to four decimal places as needed.) 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. 0 A- No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of i1 - >22 to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. 0 B- No, the formulas for the mean and standard deviation of i1 - i2 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. 0 C- 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 i1 - >22 to hold, as long as the sampling is done with replacement. 0 D- Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of i1 - >12 to hold. o. Can you conclude that the variable ;1 - i2 is normally distributed? Explain your answer. Choose the correct answer below. 0 A- No, 21 - i2 is normally distributed only if x is normally distributed on each of the two populations or ifthe sample sizes are large enough. 0 3- No, since )_( - _ must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed. 1 *2 O C- Yes, i1 - i2 is always normally distributed because of the central limit theorem. 0 D- Yes, {1 -)_(2 is always normally distributed because it is calculated using parameters