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Lubov Fominskaja [6]
3 years ago
10

How to find standard deviation from percentile for normal distribution?

Mathematics
1 answer:
QveST [7]3 years ago
8 0
The standard deviation of what?  Percentiles from any normal distribution look the same, just like the unit normal, so you can't really determine the standard deviation of the original scores. You can determine a z score from a percentile.  That tells us the number of standard deviations, positive or negative, a given score is away from the mean score.  It's a normalized test result.

Your percentile is (a hundred times) the probability that another score is less than your score.  We have a normal distribution, so that probability is the integral of the standard normal from negative infinity to our normalized score.  

Let's call the percentile rank p, already scaled between zero and 1.

p=.5 corresponds to a z score z=0 because the fiftieth percentile means we got an exactly average score, 0 standard deviations away from the mean.

We know 68% of the probability will be between -1 and +1 standard deviation.  So z=-1 corresponds to p=.5-.68/2=.16 and
z=1 corresponds to p=.5+.68/2=.84

Similarly, 95% of the probability will be between -2 and +2 standard deviations.  So z=-2 corresponds to p=.5-.95/2=.025 and
z=2 corresponds to p=.5+.95/2=.975

That's about the list I can do off the top of my head. I think three standard deviations is 99.7%. For the rest we just consult a z table or integrated normal table.  We find p in the body of the table (maybe |.5-p| depending on the table) and then the column headings tell us our z score.

In this modern age, your computer can do this for you quickly

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There is a competition in the cinema to win free tickets. You must guess the ages of the four employees. Here are the clues: - W
jenyasd209 [6]

Answer:

Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old.

Step-by-step explanation:

Let k be Kirk's age.

Let b be Brian's age.

Let m be Matt's age.

Let m_{1} be the boss/manager's age.

From the information given, we can set up 4 equations:

k+b+m+m_{1}=106

k=2(m_{1}-10)

b=2m_{1}-12

m=\frac{1}{2}m_{1}+6

Rewrite the first equation, substituting k, b, and m in terms of m_{1} to get:

2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106

Open up the parentheses using the distributive property (which is a(b-c)=ab-ac) and combine like terms to get:

5.5m_{1}-26=106

Add 26 to both sides to reach:

5.5m_{1}=132

Thus, m_{1}=24. Substitute 24 for m_{1} in the second, third, and fourth original equations to find that k=28, b=36, and m=18. Therefore, Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. To check, you can add up all of the ages to get 106.

Hope this helps :)

8 0
2 years ago
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