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

The sample of farms required should be 550 large.

Explanation:

Let the sample =K,

mean=np=100

Standard deviation=
`√(npq)`=500

probability =Z=0.90

from the normal probability formula,

Z=
`(K-np)/(√(npq))`

0.9=
`(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.