Could I have a z score of 1.00 and be in the top 85% of my class?

if the distribution is normal (bell shaped) then the mean would be at 50% and 1 sd (approx 34%) above the mean. This would put you at the 84th percentile. if its a normal distribution then n (size of class ie population) is not relevant and does not have any impact on the z-score.

For the challenge problem, why is the answer not 24.5? I got to the x - 20 = -4.5 and solved for x. Isn't x the amount of sugar in the drink we are observing?

so from x - 20 = -4.5 => x + 20 - 20 = -4.5 + 20 => x = 20 - 4.5 => x = 15.5 I think your problem was that you added 4.5 to 20 instead of subtracting 4.5. (4.5 is Negative)

I was confused what the last question was asking. Can someone explain it to me?

-.75=x-20/6 You reverse the order of finding z

Is there a z-score but based on median, not mean?

No, it is based on mean: https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/z-score/

given financial accounts, such as the profit and loss account how do I compute the Z-Score using Xcel

Grab the mean of the entire data. Do (Certain Value - Mean) / Standard Deviation

Main content

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 4

Lesson 2: Z-scores

Z-scores-problem

AP.STATS:

VAR‑2 (EU)

VAR‑2.B (LO)

VAR‑2.B.1 (EK)

VAR‑2.B.2 (EK)

VAR‑2.C (LO)

VAR‑2.C.1 (EK)

Google Classroom

Nutritionists measured the sugar content (in grams) for 32 drinks at Jake's Java coffee shop. The drinks had a mean of 18, start text, g, end text and a standard deviation of 5, start text, g, end text, and the distribution was roughly symmetric.

problem 1

A Grande Mocha Cappuccino at Jake's Java contains 14, start text, g, end text of sugar.

Calculate the standardized score (z-score) for the Grande Mocha Cappuccino.

z, equals

problem 2

What is the best interpretation of the z-score from the previous problem?

(Choice A)
This drink has 0, point, 8, start text, g, end text of sugar less than the mean of the 32 drinks.
(Choice B)
This drink is 0, point, 8 standard deviations below the mean of the 32 drinks.
(Choice C)
About 80, percent of drinks have a lower sugar content than this drink.
(Choice D)
About 80, percent of drinks have a higher sugar content than this drink.

problem 3

A different coffee shop called Ruth's Roasts serves drinks that contain a mean of 16, start text, g, end text of sugar with a standard deviation of 6, start text, g, end text.

A Grande Mocha Cappuccino at Ruth's Roasts contains 13, start text, g, end text of sugar.

Assuming that the distribution of sugar amounts have approximately the same shape, at which shop does this drink have less sugar relative to the other drinks at its respective store?

(Choice A)
This drink has relatively less sugar at Jake's Java.
(Choice B)
This drink has relatively less sugar at Ruth's Roasts.
(Choice C)
The relative sugar contents are equal at both locations.
(Choice D)
It is impossible to tell because we do not know how many drinks are offered at Ruth's Roasts.

Challenge problem

Drinks at Ben's Beans have a mean sugar content of 20, start text, g, end text with a standard deviation of 6, start text, g, end text. The sugar content in a Grande Cappuccino at Ben's Beans has a z-score of minus, 0, point, 75 compared to the rest of the drinks at that shop.

How much sugar is in a Grande Cappuccino at Ben's Beans?

grams

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ema.ukoabasi
Posted 7 years ago. Direct link to ema.ukoabasi's post “Your score was the cutoff...”
Your score was the cutoff for the top 12%. This score is known as Z= 2.0.
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(13 votes)
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Kaitlyn Anderson
Posted 5 years ago. Direct link to Kaitlyn Anderson's post “For the challenge problem...”
For the challenge problem, why is the answer not 24.5? I got to the x - 20 = -4.5 and solved for x. Isn't x the amount of sugar in the drink we are observing?
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(3 votes)
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- Lawrence
  Posted 4 years ago. Direct link to Lawrence's post “so from x - 20 = -4.5 => ...”
  so from x - 20 = -4.5 => x + 20 - 20 = -4.5 + 20 => x = 20 - 4.5 => x = 15.5
  I think your problem was that you added 4.5 to 20 instead of subtracting 4.5. (4.5 is Negative)
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  (11 votes)
Tori Leigh Rhoades
Posted 2 years ago. Direct link to Tori Leigh Rhoades's post “challenge problem, since...”
challenge problem,
since z-score=(x-mean)/std dev then
(std dev*z-score)=x-mean) equals
(std dev*z-score)+mean=x
(6*-.75)+20=15.5
-4.5+20=15.5
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(5 votes)
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Joseph Judge
Posted 4 years ago. Direct link to Joseph Judge's post “I was confused what the l...”
I was confused what the last question was asking. Can someone explain it to me?
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(3 votes)
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- Daniel T Ly
  Posted 4 years ago. Direct link to Daniel T Ly's post “-.75=x-20/6 You reverse ...”
  -.75=x-20/6 You reverse the order of finding z
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  (4 votes)
Williams, Ellie
Posted 5 years ago. Direct link to Williams, Ellie's post “Could I have a z score of...”
Could I have a z score of 1.00 and be in the top 85% of my class?
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(4 votes)
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- Ian Kerr
  Posted 5 years ago. Direct link to Ian Kerr's post “if the distribution is no...”
  if the distribution is normal (bell shaped) then the mean would be at 50% and 1 sd (approx 34%) above the mean. This would put you at the 84th percentile.
  if its a normal distribution then n (size of class ie population) is not relevant and does not have any impact on the z-score.
  Button navigates to signup page
  (3 votes)
Jeffrey Marbid
Posted 4 years ago. Direct link to Jeffrey Marbid's post “Is there a z-score but ba...”
Is there a z-score but based on median, not mean?
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(2 votes)
Answer
- Eric Xing
  Posted 4 years ago. Direct link to Eric Xing's post “No, it is based on mean: ...”
  No, it is based on mean:
  https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/z-score/
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  (4 votes)
Richard DuPont
Posted 5 years ago. Direct link to Richard DuPont's post “Thank You very much, this...”
Thank You very much, this was helpfull
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(3 votes)
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priscarnyamutenha
Posted 2 years ago. Direct link to priscarnyamutenha's post “given financial accounts,...”
given financial accounts, such as the profit and loss account how do I compute the Z-Score using Xcel
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(2 votes)
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- 384001060
  Posted 2 years ago. Direct link to 384001060's post “Grab the mean of the enti...”
  Grab the mean of the entire data.
  
  Do (Certain Value - Mean) / Standard Deviation
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  (3 votes)
WILLIAM DRAPER
Posted 6 years ago. Direct link to WILLIAM DRAPER's post “Interpret z-score in vide...”
Interpret z-score in video
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Adam Harrison
Posted a year ago. Direct link to Adam Harrison's post “Good problems! Thank you!”
Good problems! Thank you!
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