The average home price in Massachusetts is $410,000, with a standard deviation of $65,000. A city planner is studying the distribution across the state of home prices in the bottom 10%. What price will indicate that a home is in the bottom 10% if the city planner examines 200 homes around the state

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

step-by-step explanation:

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