Let d(t) be the number of dogs in the united states in year t, and let c(t) be the number of cats in the united states in year t, where t=0 corresponds to 2000.

(a.) interpret the value of p(5).

(b.) let n(t) represent the population of the united states in  year t, where t=0 corresponds to 2000. find and  interpret  h(t) = p(t) / n(t).

step-by-step explanation:

its 512 because parenthesis and to the 2nd power is 512 so it will be 512

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.