as a special promotion for a 16 ounce bottles of fruit juice, juice drink Company printed a message on the inside of each cap. Some of the cops red, better luck next time whereas others red, you own! The company advertises the promotion with the slogan one and seven wins a prize! Suppose the company is telling the truth and that every 16 ounce bottle of juice has a one and seven chance of being a winner eight friends each buy one 16 ounce bottle of juice at a local convenience store. Let X equal the number of friends who win a prize. Part A, explain why ask is a binomial variable. Part B, find the mean and standard deviation of X. Interpret each value into context. Part C, the store clerk is surprised when two of the friends when a prize. Is this group of friends just lucky, or is the company is one and seven claim in accurate? Compute P (X is less than or equal to 2) and use the result to justify your answer

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above