SOLUTION: I have a homework question that I am having trouble with understanding: Using the unit normal table, find the proportion under the standard normal curve that lies between the fo

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Question 1147305: I have a homework question that I am having trouble with understanding:
Using the unit normal table, find the proportion under the standard normal curve that lies between the following values.
(a) the mean and z= 0
(b) the mean and z= 1.96
(c) z= -1.50 and z= 1.50
(d) z= -0.08 and z= -0.50
(e) z= 1.00 and z= 2.00
.........
If someone could please explain in a step by step way to solve this problem, I have already read the chapters and I am lost.
Found 2 solutions by rothauserc, Edwin McCravy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
If you can, use a table of positive and negative z-values which lists the associated probabilities for a Normal Distribution, if you have a table with only positive z-values, you can subtract the corresponding probability from 1 and get the negative z-score probability
:
For a unit normal table, z = 1 corresponds to a proportion of 0.3413 from the mean, z = 2 corresponds to a proportion of 0.4772 from the mean and z = 0.5 corresponds to a proportion of 0.19.15 from the mean
:
(a) mean is 50% = 0.50 proportion(probability), a z=0 corresponds to 0.50 and 0.50 - 0.50 = 0
:
(b) z = 1.96, then probability(P) = 0.9750, 0.9750 - 0.50 = 0.4750
:
(c) z = -1.50 then P = 0.0668, z = 1.50 then P = 0.9332 and 0.9332 - 0.0668 = 0.8664
:
(d) z = -0.08 then P = 0.4681, z = -0.50 then P = 0.3085 and 0.4681 - 0.3085 = 0.1596
:
(e) z = 1.00 then P = 0.8413, z = 2 then P = 0.9772 and 0.9772 - 0.8413 = 0.1359
:
Note mean of a Normal Distribution means 50% of the values are above the mean and 50% of the values are below the mean
:
Note z-values correspond to standard deviations above(positive) and below(negative) from the mean
:
Note z-value = (X - mean)/standard deviation, where X is the test value, for example, suppose you want to compare someone’s weight(150 pounds) to the “average” of a population, the z-score can tell you where that person’s weight is compared to the average population’s mean weight.
:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
The standard normal curve has a z-axis instead of an x-axis.  That's because it
has 0 in the middle as the mean, and the word "zero" starts with "z".  The
values of z on the z-axis are called z-scores.

These problems are asking you what percentage (as a decimal) of the area between
the curve and the horizontal axis is shaded between the two given values on the
z-axis.  In practical problems, that percentage will be interpreted as a
probability, the probability that an event has measurement between two given
values.  You need to learn how to find these percentages by looking them up on a
table.

Go to this site and watch the video to learn how to find these values on a
table.

https://www.statisticshowto.datasciencecentral.com/tables/z-table/

-------------------------------------

(a) WHAT PROPORTION OF THE TOTAL AREA BETWEEN THE CURVE BELOW AND THE z-axis IS SHADED BETWEEN 

the mean and z = 0?  

Draw this picture: 



This is a trick question.  On the standard normal curve, the mean IS z=0,
so there is nothing to shade between z=0 and z=0, the mean and itself!

So the answer to (a) is 0 (zero).  The others, however do have shading.

-------------------------------------------

(b) WHAT PROPORTION OF THE TOTAL AREA BETWEEN THE CURVE BELOW AND THE z-axis IS SHADED BETWEEN

the mean and z= 1.96

Draw this picture:



Answer: the decimal fraction of area shaded above is 0.4750.  Watch the video to learn how to find that value.

-----------------------------------------------

(c) WHAT PROPORTION OF THE TOTAL AREA BETWEEN THE CURVE BELOW AND THE z-axis IS SHADED BETWEEN

z= -1.50 and z= 1.50

Draw this picture:



Answer: the decimal fraction of area shaded above is 0.8664.  Watch the video to
learn how to find that value from the table..

---------------------------------------------------

(a) WHAT PROPORTION OF THE TOTAL AREA BETWEEN THE CURVE BELOW AND THE z-axis IS SHADED BETWEEN 

z= -0.08 and z= -0.50

DRAW THIS PICTURE:



Answer: the decimal fraction of area shaded above is 0.1596.  Watch the video to learn how to find that value.

--------------------------------------

(e) 

(a) WHAT PROPORTION OF THE TOTAL AREA BETWEEN THE CURVE BELOW AND THE z-axis IS SHADED BETWEEN 

z= 1.00 and z= 2.00 

DRAW THIS PICTURE:



Answer: the decimal fraction of area shaded above is 0.1359.  Watch the video to
learn how to find that value.

If you have any questions, ask me in the space below and I'll get back to you by
email.  There is never any charge as I do this for fun.

Edwin
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