If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## 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)
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?

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?

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

## Want to join the conversation?

• Your score was the cutoff for the top 12%. This score is known as Z= 2.0.
• 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)
• 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
• 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
• 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.
• Is there a z-score but based on median, not mean?