Q:

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

Accepted Solution

A:
Answer: B. 461 acresStep-by-step 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.$$P(x>190)=P(\dfrac{x-\mu}{\sigma}>\dfrac{190-185.2}{23.5})$$[Formula : $$z=\dfrac{x-\mu}{\sigma}$$]$$=P(z>0.2043)=1-P(z<0.2043)$$ Β [β΅ P(Z>z)=1-P(Z<z)]$$1-0.5809405$$ Β  [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 :-$$0.4190595\times1100=460.96545\approx461\text{ acres}$$hence, the correct answer is B. 461 acres .