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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
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

problem 2
What is the best interpretation of the z-score from the previous problem?
Choose 1 answer:
Choose 1 answer:

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?
Choose 1 answer:
Choose 1 answer:

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?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
grams

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