Answer:
Explanation:
Hello!
The variable of interest is
X: Time it takes to sell a house in St. Lois
n= 28 houses
X[bar]= 220 days
σ= 40 days
a) To be able to apply the central limit theorem you have to use a large enough sample. As a rule, most statistic courses consider a sample size n≥30 to be large enough for the approximation.
You can always just assume that the population has a normal distribution if you had the raw information of the sample you could conduct a test to see if it comes from a normal population or not.
The sample taken is n=28, so in theory, you cannot apply the central limit theorem. Best is to assume the population is normal-
b) So assuming that the population has a normal distribution, the formula for the CI is:
X[bar] ±
*


220 ± 1.648 *

[207.54; 232.46]days
With a confidence level of 90%, you'd expect that the interval [207.54; 232.46]days will contain the true average time it takes to sell a house in St. Lois, Missouri.
I hope it helps!