A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. a. For independent samples of sizes 9 and 4, respectively, find the mean and standard deviation of x1 - x2.b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer.c. Can you conclude that the variable x1 - x2 is normally distributed? Explain your answer.

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Solve only the part a, b and c for question 10.

What is the population standard deviation using the following formula

The scores of the Betropolis University Music Appreciation Exam are Normally Distributed with a mean of 50 and a standard deviation of 10; that is N(50, 10). A. Boris scored 40.6 and Bela scored 56.8. Find the percent of students who scored greater than Boris and less than Bela. Your answer should be correct to 4 places after the decimal point. ___________ B. 51% of the students score greater than Bernie. Find Bernie’s score. Your answer should be correct to 3 places after the decimal point. Bernie’s score was ___________

B Choosing a topic Sk.. For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula 1 where p is the minimum percentage of scores that fall within k k2 is p = 1 - standard deviations on both sides of the mean. Use this formula to answer the following questions. a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 2.2 standard deviations on both sides of the mean? b) If you have scores that are normally distributed, find the percentage of scores that fall within 2.2 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 64 percent of the scores? Note: To answer part c you will need to solve the equation for k.