During each week of piano lessons, Justin learns to play 2 new pieces. In all, how many weeks of piano lessons will Justin need before he will be able to play a total of 46 pieces?

23 weeks

Step-by-step explanation:

For 1 week he can learn 2 new pieces. He wants to pay 46 pieces. So we would make the following equation:

where x is equal to the number of weeks

We can then solve for x by dividing 46 by 2.

So in order for Justin to learn 46 pieces, it would take 23 weeks.

step-by-step explanation:

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.