Answer:
a) [92.8 , 477.04]
b) [69.611, 500.229]
Step-by-step explanation:
The mean and standard deviation of the sample can be computed by using the definition formulas and we obtain
mean
[tex]\large \bar x[/tex] = 284.9165 ≅ $284.92
standard deviation
s = 96.0639 ≅ $96.06
a)
Roughly speaking, we could say that a 95% confidence interval is given by the 68–95–99.7 rule for the Normal Distribution, which states that around 95% of the data is between [tex]\large \bar x[/tex] -2s and [tex]\large \bar x[/tex] +2s. So, an informal 95% confidence interval would be
[284.92 - 2*96.06, 284.92 + 2*96.06] = [92.8 , 477.04]
b) If the data are assumed from [tex]\large N(\mu ,\sigma ^2)[/tex], then the 95% confidence interval is given by [A, B] where A, B are values such that the area under the normal curve [tex]\large N(284.92 ,96.06 ^2)[/tex] outside the interval [A, B] is less than 5% or 0.05 (see picture attached).
This value can be found with the help of a calculator or computer, and we find
[A, B] = [69.611, 500.229]
