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
= 284.9165 ≅ <em> $284.92
</em>
standard deviation
s = 96.0639 ≅ <em>$96.06
</em>
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 -2s and +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 , then the 95% confidence interval is given by [A, B] where A, B are values such that the area under the normal curve outside the interval [A, B] is <em>less than 5% or 0.05</em> (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]