Answer:
The range of true mean value is "[tex]6.92 \pm 1.11142[/tex]".
Explanation:
The given values are:
Number of bricks,
n = 15
Variance,
σ² = 6.89 MN/m²
Mean,
[tex]\bar{x} = 6.92 \ MN/m^2[/tex]
90% confidence level,
z = 1.64
Now,
The margin of error will be:
= [tex]z\sqrt{\frac{\sigma^2}{n} }[/tex]
On substituting the given values, we get
= [tex]1.64\sqrt{\frac{6.89}{15} }[/tex]
= [tex]1.64\times 0.6777[/tex]
= [tex]1.11142[/tex]
So,
Range of true mean value will be:
= [tex]Mean \pm Margin \ of \ error[/tex]
= [tex]6.92 \pm 1.11142[/tex]
