MATH SOLVE

8 months ago

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. [tex]\mu=185.2\ \ , \ \sigma=23.5[/tex]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.[tex]P(x>190)=P(\dfrac{x-\mu}{\sigma}>\dfrac{190-185.2}{23.5})[/tex][Formula : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]][tex]=P(z>0.2043)=1-P(z<0.2043)[/tex] [∵ P(Z>z)=1-P(Z<z)][tex]1-0.5809405[/tex] [using z-value calculator or table][tex]=0.4190595[/tex]Now, If a study included 1100 acres then the expected number to yield more than 190 bushels of corn per acre :-[tex]0.4190595\times1100=460.96545\approx461\text{ acres}[/tex]hence, the correct answer is B. 461 acres .