A set of piano prices distributed at a mean of 3000 and a standard deviation of 200 dollars. An electric piano has a price of 2576 dollars. What proportion of piano prices are higher than the price of the electric piano?

The proportion of piano prices higher than the electric piano is 98.3%

Step-by-step explanation:

The first thing to do here is to calculate the standard score of the price of the electric piano given.

Mathematically, this is

z-score = (x-mean) / SD

where mean is 3000 and SD is 200, x is 2576

z-score = (2576-3000) / 200 = - 2.12

Now we proceed to calculate the probability of this z-score

The probability we are trying to calculate is

P (x > $2576) or simply P (z > - 2.12)

Using standard score probability calculator or table, we have

P (x>2576) = 1 - P (x<2576)

But, P (x<2576) = 0.017003

P (x>2576) = 1 - P (x<2576) = 0.983

This is same as 98.3%