Answer:
And replacing the value obtained we got:
And if we solve for a we got
Step-by-step explanation:
Let X the random variable that represent the average home prices of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
We want to find a value who accumulate 0.10 of the area on the left and 0.90 of the area on the right of the normal standard distributon and for this case it's z=-1.282
And using the distribution for the sample mean we can do this:
And replacing the value obtained we got:
And if we solve for a we got