Answer Happy

A variable of two populations has a mean of 20 and a standard deviation of 24 for one of the populations and a mean of 20 and a standard deviation of 15 for the other population. Moreover, the variable is normally distributed on each of the two populations. Complete parts (a) through (c). a. For independent samples of size 4 and 9, respectively, determine the mean and standard deviation of X₁ -X₂. The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁ -X₂ is. (Round to four decimal places as needed.) b. Can you conclude that the variable x₁ - x₂ is normally distributed? Explain your answer. Choose the correct answer below. C O A. No, since X₁ -X₂ must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed. O B. Yes, since the variable is normally distributed on each of the two populations, x₁-x2 is normally distributed. O C. No, X₁-X₂ is normally distributed only if the sample sizes are large enough. O D. Yes, X₁ -X₂ is always normally distributed because of the central limit theorem. c. Determine the percentage of all pairs of independent samples of sizes 4 and 9, respectively, from the two populations with the prope that the difference x₁-x₂ between the sample means is between - 13 and 13.