Mark B. answered • 01/08/18
Tutor
New to Wyzant
PhD candidate with strong statistics and tutoring experience.
Hello,
Okay, the first step you need to do is to convert your value of 222.6 to a z-score.
So, let's do that, fair enough?
z = Value of score - Mean
------------------------
Standard Deviation
(My apologies, but I cannot seem to find the characters to give you for mean - M - and standard deviation - omega).
z = 222.6 - 225.5
Okay, the first step you need to do is to convert your value of 222.6 to a z-score.
So, let's do that, fair enough?
z = Value of score - Mean
------------------------
Standard Deviation
(My apologies, but I cannot seem to find the characters to give you for mean - M - and standard deviation - omega).
z = 222.6 - 225.5
-------------------
3.2
When you calculate the above, you arrive at the following value: -90625
Every statistician has their own preference here, but personally I would round up to -91.
Now, go to a z-score table which has both negative and positive values. I will give you a link immediately below:
http://www.z-table.com/
Okay, now we can get some pertinent information to assist us in answering the problem, okay? To find the probability (or as your answer requests, a 4 decimal place number) what you do is start from the bottom of the z score table (the negative value one because our answer is negative, correct?
Doing so, you go to -.9 which is located all of the way to the LEFT SIDE of the table and is the first column. Do you see it?
Once you locate THAT, you now need to look at the top row of the table where the values are .00, .01, .02, etc.
Remember our answer we arrived at when calculating to a z-score was -.91 therefore, you want to go the the row under .01 because it is the hundredths, right? In other words, if you take -0.9 on the left side of the table you need to add the hundredths to the answer. When you go down the table under the .01 column look for the INTERSECTION between the row -0.9 AND the column under .01 and when you do, you will find the following value:
.1814 Please go through the exercise of locating this as it will make this easier for you later in the term.
NOW PLEASE REMEMBER THIS: The value you just arrived at is for ALL values to the LEFT of the score. If you look at the top of that chart you will see the normal bell curve with part of it shaded gray, right. The gray area is what you just located.
But your question is to find the probability that a randomly selected value is GREATER than the value we just found for 222.6, correct? We merely transformed the value into a z score to handle it easier.
The entire area under that normal bell curve is 1.0000 so in order to determine the probability that the value falls to the RIGHT of that z-score we just calculated, we must subtract our obtained value of .1814 from 1.0000.
Do you understand why now? If not please do a follow up question or response.
When you subtract .1814 from 1.0000 you arrive at .8186.
To proof your work, when you add the two values, (.1814 plus .8186) they should equal 1.0000 And, in fact they do.
Your answer as a number to four decimal places is .8186.
I hope this helps you and you understand the WHY behind our answer. Have a great day tomorrow.
3.2
When you calculate the above, you arrive at the following value: -90625
Every statistician has their own preference here, but personally I would round up to -91.
Now, go to a z-score table which has both negative and positive values. I will give you a link immediately below:
http://www.z-table.com/
Okay, now we can get some pertinent information to assist us in answering the problem, okay? To find the probability (or as your answer requests, a 4 decimal place number) what you do is start from the bottom of the z score table (the negative value one because our answer is negative, correct?
Doing so, you go to -.9 which is located all of the way to the LEFT SIDE of the table and is the first column. Do you see it?
Once you locate THAT, you now need to look at the top row of the table where the values are .00, .01, .02, etc.
Remember our answer we arrived at when calculating to a z-score was -.91 therefore, you want to go the the row under .01 because it is the hundredths, right? In other words, if you take -0.9 on the left side of the table you need to add the hundredths to the answer. When you go down the table under the .01 column look for the INTERSECTION between the row -0.9 AND the column under .01 and when you do, you will find the following value:
.1814 Please go through the exercise of locating this as it will make this easier for you later in the term.
NOW PLEASE REMEMBER THIS: The value you just arrived at is for ALL values to the LEFT of the score. If you look at the top of that chart you will see the normal bell curve with part of it shaded gray, right. The gray area is what you just located.
But your question is to find the probability that a randomly selected value is GREATER than the value we just found for 222.6, correct? We merely transformed the value into a z score to handle it easier.
The entire area under that normal bell curve is 1.0000 so in order to determine the probability that the value falls to the RIGHT of that z-score we just calculated, we must subtract our obtained value of .1814 from 1.0000.
Do you understand why now? If not please do a follow up question or response.
When you subtract .1814 from 1.0000 you arrive at .8186.
To proof your work, when you add the two values, (.1814 plus .8186) they should equal 1.0000 And, in fact they do.
Your answer as a number to four decimal places is .8186.
I hope this helps you and you understand the WHY behind our answer. Have a great day tomorrow.
REMEMBER THIS: To obtain the probability that a value will exceed that z score you MUST subtract whatever value you are discussing (for this type of problem) from the total area under the bell curve which is 1.0000 (four decimal places per your request).
