6.2 Normal Model

Question 1

Percentile meaning

Answer 1

Relative frequency
Any value (x/ value of NV) within this range (10%) isn’t necessarily representative of it as a whole, but GAUGED through its representation of being a range OF that value that is AT or BELOW
10% of ALL values of NVs are at or below the GIVEN value
Gauging the closeness between the GIVEN value and the rest of the values
!!!
The range contains the given but it also represents the stopping point, where the OTHERS (all) fall, and where the OTHERS are placed above it (subtract percentile from 100%)
!!! REMEMBER WHEN SUBTRACTING FROM 100- each number HAS to have a % after it on calc

Question 2

Standard deviation and relative frequency

Answer 2

Super tall height of a curve means SMALL standard deviation (all the girls are like each other- KW ALL/ a lot of dots)

Question 3

Symbols of normal model

Answer 3

Probability- the area under the curve. THIS IS ABT POP Use empirical rule or stat crunch
For continuous NVs
Mu- Mean of a probability distribution
(X_ is about a data set)
Sigmas- SD of probability distribution ( s for SD was for sample)
Normal curve= N(mean, SD) (N is normal distribution)
!!!
With percentiles, we are no longer looking at samples, but probability distribution (not exactly ALL either)
!!!! N(96, 3) = normal mode is 96 mean and 3 SD

Question 4

Review for UD

Answer 4

Mean meaning
SD meaning
Median meaning
Z scores- SDs but not in number form (3.5= 1 SD or z-score)
Rates

Question 5

Finding probability (percentage, not exactly percentile) tips

Answer 5

They’ll ask for the translation of the z-scores to standard deviation values (mean +- SD )
FP - also what percentage is greater/ less than x value (not percent)-> 100-95
FP *for ER (falling on tick mark)- always divide in half because it asks for ONE side
FP - between these two x values? -> use the empirical rule section values
!!! Can be in decimal form and not in percent?? (5, B)

Question 6

Empirical rule section values

Answer 6

2.35% (2.5) 13.5% 34%

• may need to straight up add 13.5 and 34 to get a probability (47.5%)

Question 7

100- 99.7

Answer 7

Is about 0% when you divide the difference by 2 BUT WHEN NOT MULTIPLE CHOICE- actual percent (0.15%-> NOT 15%- see first card)

Question 8

Not everything fits ER- statcrunch

Answer 8

When the x-values dont land exactly on a tick mark (SD)
Stat- calc- normal
!!!!
“X)
* probability of that number to be more or less THAN THE MEAN (X)

When you want the other side (less but now more), 1 whole distribution - given decimal (for other side)

BETWEEN- switch to between
* make sure its lower to upper (as it reads in question)

Question 9

Two values on graph

Answer 9

“Between -2 SDs and 2 SDs”

Question 10

Finding probability/ percentile from GIVEN measurement

Answer 10

Measurement is given-> put in parentheses, but since this translates to definition of percentile, make sign <_ (less than)

Question 11

Data value inquired

Answer 11

x
The value they want you to find probability of IT being above and below the mean (the average/ everyone else’s score)
the mean is less than or equal to the value= the average of the scores (proportion-> successes/ total) is less than or equal to it
THAT is the probability (being less or more), all based on the TOI proportion

Question 12

Percentile (finding percentile)- we dont find percentile without SC, just percentage

Answer 12

FM- “You are in the 75th percentile”- They either score the same as you or below (you beat out 75% of the people)
- “75 percent taller or shorter than that person/ NV”
- IMP !!!!! Need include in explanation that 75th percentile= people here are 75% more able to TOI (context) than pop
- OR
(Find those that are above by calculation)

FM- “Find exact value at 90th percentile”
FP- “shorter/ bigger than x-value” -> find probability (%) LESS or MORE than 2.4”
!!! FP- “At least as long as” -> actually MORE . . . >_
FM- “Top 15%” = 85th percentile BUT you MUST make it .15 and flip the sign to more (>) !!! So think of TOP (>) 15% (0.15)
FP-> “Scored HIGHER than what percentage” -> X<_ score
!!!We use less than _ its teh standard percentile meaning . We found the percentile by inputting less than, so everyone underneath is who they scored HIGHER than

Question 13

Probability vs percentile

Answer 13

Probability is the percentage (percentile area)

Question 14

Percentile trick question (2, B) FM

Answer 14

FM- “15 percent of all men 20 years and up are above what height?”
Its just what youre thinking !
Since percentiles (percents) represent BELOW and equal, since this asks for ABOVE, just find the “other side” -> 100-15% -> the number at the 85th percentile/ they are in the 85th percentile because they taller than everyone below them (under 85th)

Question 15

When i thought it was 100% (2, C and D)

Answer 15

FP- It was actually 90% which makes sense because like just because they’re literally between all the values (heights), the first percent is 5, and the last is 95, so 5+5= 10 -> 100-10= 90
When its not cut and dry-> start at 5th but dont count IT as a 5%, count its jump from 5th to 10th as the 5%, repeat til get to 50th
So the number that represents the percentile is the starting and ending point respectively for “betweens”

!!! So 5th is “this number and below” OR just “below, this percentile can also classify explicitly ONLY those below it, not IT”

Question 16

Side note (mean vs median)

Answer 16

We-re using mostly mean hear because the distributions are normal/ symmetric

Question 17

Prob symbols meanings

Answer 17

X < 437 means the probability of that a person scores LESS than 43, all this determined though COMPARED by proportion (X) === then this is further concretely described as a percent (=0.25)
More than= X> 437

Question 18

Z-scores in probability distrubutions

Answer 18

“Standard scores”

Question 19

Confusion - (7, B)

Answer 19

Empirical rule but I had to use stat crunch- I got 32% at first —-OMG I forgot to divide that by two duh-> 16%

Question 20

FP anything not in between

Answer 20

FP- “Percentage that WONT fit in the “inbetween” area -> find on ER, then subtract that in between (whole process to find between) from 100
!!!IMPPP FP- Dont need to divide by 2 because they’re asking for both sides, not just one (would ask for “less” than the in between FE)

Question 21

KEY TIP for reading across the SEs line

Answer 21

Look at it like a number line

Question 22

Actuallyfinding MEASURMENT (x-value)

Answer 22

First portion of percentile card
“80th percentile’’ means 80 and below (<_) but put the 80 in decimal form (0.8)

Question 23

Measurement vs probability

Answer 23

Measurement is basically the x-value in the parentheses and not the percent AND not asking what is more or less from this x-value, just what number it is
!!!!FM- Will ask what the ER percent equals to as SD value- ONLY if % is in question-> CANT answer for PERCENTILE (for finding measurement)
- if they ask for “what number is the number that would be MORE than ER %”

Question 24

Confused

Answer 24

When do I leave answer as decimal or as percent? - its just a probability

Question 25

Gist

Answer 25

FM- If question has %, it wants the measurement/ x value (not likely)
When there IS %, it will asks what this x-value is based on MORE or LESS of
Find percentile tick mark->

Question 26

Rates with percentiles

Answer 26

Find average joe (per) number
Proportion:
TOI CV / sample size (total) = a percent (find percent through percentile) -> MULTIPLY by average joe