The average number of miles (in thousands) that a car's tire will function before needing replacement is 60 and the standard deviation is 16. Suppose that 11 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution a. What is the distribution of X X NO b. What is the distribution of a?o - N c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65.2 and 67.8. d. For the 11 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65.2 and 67.8. e. For part d), is the assumption that the distribution is normal necessary? No Yes​

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