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 1100 acres, about how many would be expected to yield more than 190 bushels of corn per acre?

A. 639 acresB. 461 acresC. 419 acresD. 503 acres

Answer 1

Answer: B. 461 acres

Explanation:

Given : 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.

i.e.
`\mu=185.2\ \ , \ \sigma=23.5`

Let x denotes the amount of corn yield.

Now, the probability that the amount of corn yield is more than 190 bushels of corn per acre.

`P(x>190)=P((x-\mu)/(\sigma)>(190-185.2)/(23.5))`

[Formula :
`z=(x-\mu)/(\sigma)`]

`=P(z>0.2043)=1-P(z<0.2043)` [∵ P(Z>z)=1-P(Z<z)]

`1-0.5809405` [using z-value calculator or table]

`=0.4190595`

Now, If a study included 1100 acres then the expected number to yield more than 190 bushels of corn per acre :-

`0.4190595*1100=460.96545\approx461\text{ acres}`

hence, the correct answer is B. 461 acres .