Respuesta :
Answer:
A sample size of 12 is needed.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation(square root of the variance) [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
[tex]\sigma = \sqrt{25} = 5[/tex]
How large must the sample size be if we want the standard error of the sample average to be at most 1.5
We need n for which s = 1.5.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.5 = \frac{5}{\sqrt{n}}[/tex]
[tex]1.5\sqrt{n} = 5[/tex]
[tex]\sqrt{n} = \frac{5}{1.5}[/tex]
[tex](\sqrt{n})^{2} = (\frac{5}{1.5})^{2}[/tex]
[tex]n = 11.11[/tex]
Rounding up
A sample size of 12 is needed.
