SOLUTION: How large should the size of a random sample be so that we can be 90% certain that the sample mean X will not deviate from the true mean by more than σ/2? thank you

Question 1178274: How large should the size of a random sample be so that we can be 90% certain that the sample mean X will not deviate from the true mean by more than σ/2?
thank you
Found 2 solutions by Boreal, ewatrrr:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the error, e,=sigma/sqrt(n)*z(0.95)
e^2=2.706*sigma^2/n, squaring everything including z=1.645
e=sigma/2 so e^2=sigma^/4
so sigma^2/4=2.706 sigma^2/n
n=10.0824 or 11.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
90% certain: z = 1.645

0r

n = 11 (rounding up to next whole number)
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