There were 370 people at a play. the admission price was $2 for adults and $1 for children. the admission receipts were $560. how many adults and how many children attended?

Set up equations: let c be # of children, and a be # adults:

c + a = 370

c + 2a = 560

solve:

c-c + 2a - a = 560-370

a = 190

so

c = 370 - 190 = 180

190 adults and 180 children attended.

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.