Ellie practices piano 23 h per day, several days each week. she practiced piano 3223 hours during the summer. what equation can be used to find the number of days that she practiced piano during the summer? let d represent the number of days. drag and drop the appropriate number into each box.

d = 140

3223h/23h (Per day) = d

3223 / 23 = 140.130434783

d = 140.130434783 days

or d = 140 days simplified

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.