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10. An estimate is needed of the mean acreage of farms in Manitoba, Canada. The estimate should be correct to within 100 acres with probability 0.90. A preliminary study suggests that 500 acres is a reasonable guess for the standard deviation of farm size. How large a sample of farms is required?

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Answer:

The sample of farms required should be 550 large.

Step-by-step explanation:

Let the sample =K,

mean=np=100

Standard deviation=[tex]\sqrt{npq}[/tex]=500

probability =Z=0.90

from the normal probability formula,

Z=[tex]\frac{K-np}{\sqrt{npq}}[/tex]

0.9=[tex]\frac{K-100}{500}[/tex]

500 X 0.9=K-100

450=K-100

K=450+100=550

Hence, the sample of farms required should be 550 large.

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