Answer:
A sample size of 12 or more will give a standard error of atmost 1.5.
Step-by-step explanation:
We are given the following in the question:
Population mean = 100
Variance = 25
[tex]\sigma^2 = 25\\\sigma =\sqrt{25} = 5[/tex]
Thus, the standard deviation is 5.
Formula:
Standard error =
[tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting values, we get,
[tex]\dfrac{\sigma}{\sqrt{n}} \le 1.5\\\\\dfrac{5}{\sqrt{n}} \leq 1.5\\\\\Rightarrow \sqrt{n} \geq \dfrac{5}{1.5}=3.33\\\\\Rightarrow n \geq 11.11\\\Rightarrow n = 12[/tex]
Thus, a sample size of 12 or more will give a standard error of atmost 1.5.
