SOLUTION: The mean price of new homes from a sample of houses is $165,000 with a standard deviation of $21,000. The data set has a bell-shaped distribution. Between what two do 95% of the ho

Question 1204348: The mean price of new homes from a sample of houses is $165,000 with a standard deviation of $21,000. The data set has a bell-shaped distribution. Between what two do 95% of the houses fall?
Using the sample statistics from above, find the z-scores of each of the following house prices.
a. $202,000
b. $70,000
c. $175,000
d. $137,000
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

for middle % values ; critical value of = ±

therefore corresponding lower end value is

and upper end value

% of the houses fall between prices $ and $

a. $

b. $

c. $

d. $

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll leave problem 1 for the student to do.
Hint: The value 1.96 is involved somehow.

I'll focus on part (a) of the 2nd question.

Since every value is in thousands, we can ignore the trailing triple zeros at the end. They'll cancel out anyway.
For example, think of $202,000 as just 202.

Let's compute the z score
z = (x - mu)/sigma
z = (202 - 165)/21
z = 1.76190476190477
z = 1.76
This is the approximate number of standard deviation units that we are above the mean.

In many Z tables, perhaps all of them(?), it's customary that the z scores are rounded to two decimal places.
Here's an example of one such table
https://www.ztable.net/

The calculations for parts (b) through (d) will follow the same template of steps.
Please let me know if you have questions about any of the steps shown above.

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