Question

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?

Answer 1

Answer:

The sample of farms required should be 550 large.

Step-by-step explanation:

Let the sample =K,

mean=np=100

Standard deviation=$\sqrt{npq}$=500

probability =Z=0.90

from the normal probability formula,

Z=$\frac{K-np}{\sqrt{npq}}$

0.9=$\frac{K-100}{500}$

500 X 0.9=K-100

450=K-100

K=450+100=550

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