Question

In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 206 bushels of corn per acre?

Answer 1

Given,

= 185.2 , = 23.5

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

So,

P(X > 206) = P(Z > ( 206 - 185.2) / 23.5)

= P(Z > 0.885)

= 0.1881 (From Z table)

Of the 1200 acres we expect, 1200 * 0.1881 = 225.7 acres yield more than 206 bushels of corn per acre.