anonymous
  • anonymous
Heelllp, I am frustrated... Use the normal distribution of SAT critical reading scores for which the mean is 513 and the standard deviation is 110. Assume the variable x is normally distributed. a)What part of the SAT verbal scores is less than 650? b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575? I am sooooooo, lost an confused. Please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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amistre64
  • amistre64
your going to need a ztable or a stats calculator
amistre64
  • amistre64
\[z=\frac{x-\bar x}{sd}\]
anonymous
  • anonymous
I've downloaded a normal standard table.

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amistre64
  • amistre64
\[z=\frac{650-513}{110}\]
Directrix
  • Directrix
For a, the z-score = (650 - 513)/110 = 1.245 for the z-score. Now, to the table.
amistre64
  • amistre64
this gives the zscore for x = 650
amistre64
  • amistre64
different tables express this in different ways
amistre64
  • amistre64
at any rate, you are over 50%
anonymous
  • anonymous
Should I round the 1.245 to 1.3?
amistre64
  • amistre64
that would be fine
amistre64
  • amistre64
if that value is less than .5 on yout table; than just add the .5
anonymous
  • anonymous
.8944 is what I see when I look at the normal standard table? What do I to with that to get .5, that you you have
Directrix
  • Directrix
The area under the standard normal curve between z = 0 and z = 1.25 = .3944. Add .5 to that to get .8944 as the area under the curve below a z of 1.23. 89.44% of scores are less thatn 650
amistre64
  • amistre64
since that value is greater than .5; that tells me your table is measureing things from the left tail and not the mean itself
amistre64
  • amistre64
this same concept is applied to part b; but with the notion that you are aware of what the area it is your looking for is definedq
Directrix
  • Directrix
I'm using the table at this link: http://www.mathsisfun.com/data/standard-normal-distribution-table.html
amistre64
  • amistre64
|dw:1333312575004:dw| in the second part they expect you to knnow that you are looking for 1 - table value for the shaded region
Directrix
  • Directrix
At the top of any standard normal distribution area table is an icon telling what the areas in the table mean. A user adjusts to that.
amistre64
  • amistre64
as long as they are aware of what information the icon is actually presenting :)
amistre64
  • amistre64
my stats teacher was more focused on a ti83 than tables, so i had to pick that up on me own
Directrix
  • Directrix
I'm getting 287.7 or 288 for part b. Will await confirmation before posting work.
Directrix
  • Directrix
@amistre64 --> Oh, I understand your concern about the table now.
anonymous
  • anonymous
I am a little behind. The link you sent result is .3944, the one I used gave a result of .8944? How is that?
amistre64
  • amistre64
if the zscore is measured from the mean; then we have to interpolate for where it is that we want to be; and since we are on the right of the mean, we already have .5 to deal with; the .3944 is the extra stuff to tack on
amistre64
  • amistre64
if the zscore is measured from the tail; then it already has the .5 in it and gives a distances from the left side already
Directrix
  • Directrix
It is coming from how to interpret this icon at top of table.
amistre64
  • amistre64
the tables are not standard by any means; so you have to know what your specific the table is telling you
anonymous
  • anonymous
ok...Where or how did you get .5?
Directrix
  • Directrix
@LynDor22 --> I had to add in the .5 to the left of the mean at z = 0.
amistre64
  • amistre64
the mean measure is .5 from the left
amistre64
  • amistre64
|dw:1333313205023:dw|
Directrix
  • Directrix
The area under the curve is 1 with .5 to the left of the mean of z = 0 and .5 to the right.
amistre64
  • amistre64
|dw:1333313261083:dw|
anonymous
  • anonymous
Oh wow...This is more complex than I thought
amistre64
  • amistre64
not really; its just the different authors use a different format for their tables
Directrix
  • Directrix
@amistre64 --> The word "Standard" does not modify "Table" but the "Normal Curve" as in "Standard Normal Curve.
amistre64
  • amistre64
:) yes
amistre64
  • amistre64
the idea tho, is to know what it is your measureing in order to use any table efficiently to find a result
amistre64
  • amistre64
if i ask whats the distance from california to boston; some authors feel that the distance is the actual measure of cali to boston; others feel that if you know the distance from cali to kansas that you only really need the distance from kansas to boston to determine the overall distance :)
Directrix
  • Directrix
@LynDor22 --> Post the link to the table you are using. Maybe we can cut through the confusion by all getting on the same table.
anonymous
  • anonymous
Part A is 89.35% How do I get part B
Directrix
  • Directrix
b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575? Get the z-score using the formula. z = (575 -513) /110 = .563. Do you agree so far?
anonymous
  • anonymous
yes
Directrix
  • Directrix
We have to find z = .563 (above the mean of 0) and find the area under the curve associated with z = .563 and above. Our task is to the the area from z = .563 to the right tail because the question asks about scores above 575.
Directrix
  • Directrix
@LynDor22 --> What areas are you getting under the curve table?
Directrix
  • Directrix
Directrix
  • Directrix
|dw:1333315986871:dw|

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