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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

mu=165000+
sigma=21000

for middle 95% values ; critical value of z+ = ±1.96+

therefore corresponding lower end value is
mu%2Bz%2Asigma+=165000-1.96%2A21000+=123840
and upper end value
mu%2Bz%2Asigma+=165000%2B1.96%2A21000+=206160

95% of the houses fall between prices $123840 and $206160




a. $202000

165000++%2Bz%2A21000+=202000
z%2A21000+=202000-165000+
z%2A21000+=37000
z+=37000%2F21000
z+=37%2F21
z+=1.7619


b. $70000
165000++%2Bz%2A21000+=70000
z%2A21000+=70000-165000+
z%2A21000+=-95000
z+=-95000%2F21000
z+=-95%2F21
z+=-4.5238


c. $175000
165000++%2Bz%2A21000+=175000
z%2A21000+=175000-165000+
z%2A21000+=10000
z+=10000%2F21000
z+=10%2F21
z+=0.47619


d. $137000
165000++%2Bz%2A21000+=137000
z%2A21000+=137000-165000+
z%2A21000+=-28000
z+=-28000%2F21000
z+=-28%2F21
z+=-4%2F3
z=-1.3333




Answer by math_tutor2020(3817) About Me  (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.