Let be the function that assigns to each nonnegative integer its last digit. note: the nonnegative integers is the set of positive integers along with zero, or all of the integers except for the negative integers. what is the domain of ?

The domain of a function is the complete set of possible values of the independent variable. In this case, the independent variable is any nonnegative integer. The nonnegative integers are the set of positive integers along with zero, then,

domain = {0, 1, 2, 3, ...} = natural numbers.

its kinda hard to answer this when we dont have all the information that we need.

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.