Answer:
The way to represent this it is
[tex] 12.33 - \frac{0.27}{\sqrt{n} } < \mu < 12.33 + \frac{0.27}{\sqrt{n} } [/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is
The standard deviation is
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100-95)[/tex]
[tex]\alpha = 0.05[/tex]
The critical value for [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table that value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Now the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }[/tex]
[tex]E = \frac{0.27}{\sqrt{n} }[/tex]
Now the error range to show a 95% confidence is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
[tex] 12.33 - \frac{0.27}{\sqrt{n} } < \mu < 12.33 + \frac{0.27}{\sqrt{n} } [/tex]
Here notice that the significant figure is keep to three to match the significant figure of the given values
