A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times. Let x¯1 x ¯ 1 represent the average of the first ten rolls, and let x¯2 x ¯ 2 represent the average of the remaining five rolls. What is the mean μ(x¯1−x¯2) μ ( x ¯ 1 − x ¯ 2 ) of the sampling distribution of the difference in sample means x¯1−x¯2 x ¯ 1 − x ¯ 2 ?

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.