Grade 11 · Math · Algebra 2

11th grade Z-scores and normal probabilities worksheet

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z-scores and normal probabilities

Grade 11 Math Worksheet - Challenge Me

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z-table: an area of 0.9 to the left matches z = 1.28. Scores on Bo's class quiz are normal with mean 70 and SD 8. To the nearest tenth, what score marks the edge of the top 10%?
z-table: an area of 0.05 to the left matches z = -1.645. Paper-airplane flights in Esme's class are normal with mean 150 cm and SD 20 cm. To the nearest tenth, what flight marks the edge of the bottom 5%?
z-table: an area of 0.97 to the left matches z = 1.88. Jump heights in Jun's class are normal with mean 40 cm and SD 6 cm. To the nearest tenth, what height marks the edge of the top 3%?
z-table: an area of 0.2 to the left matches z = -0.84. Puzzle times in Kira's class are normal with mean 12 minutes and SD 1.5 minutes. To the nearest tenth, what time marks the edge of the bottom 20%?
A 36-second lap in Milo's class has a z-score of -1.5, and the mean is 48 seconds. What is the standard deviation?
A 180 cm jump in Noah's class has a z-score of 2.5, and the mean is 150 cm. What is the standard deviation?
A 7.5-hour flashlight in Pia's class has a z-score of 0.75, and the mean is 6 hours. What is the standard deviation?
z-table (area to the left): z = 1.50: 0.9332. Ren helps weigh 500 eggs; the weights are normal with mean 60 g and SD 4 g. To the nearest whole number, about how many eggs are above 66 g?
z-table (area to the left): z = 1.25: 0.8944. Tala helps weigh 800 apples; the weights are normal with mean 150 g and SD 16 g. To the nearest whole number, about how many apples are below 130 g?
z-table (area to the left): z = 1.20: 0.8849. Ari reads a test of 1,200 bottles; the fills are normal with mean 500 mL and SD 2.5 mL. To the nearest whole number, about how many bottles are above 503 mL?

11th grade Z-scores and normal probabilities worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Z-scores and normal probabilities. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find a z-score and turn a z-score back into a value.
I can read a z-table for areas above, below and between values, using symmetry for negative z.
I can compare results from different groups by z and find a value from a percent.

Standard: S-ID.A.4

Words to know

z-score: How many SDs a value sits from the mean; negative below it.

z-table: A list of areas to the left of each z.

symmetry: The area left of −z equals the area right of z.

relative standing: How a result compares with its own group.

percentile: The percent of values below a value.

Common mistakes

Flipped the sign of a z-score: a value below the mean has a negative z. Point to the value on a drawn curve together and say which side it is on.

Used the gap from the mean without dividing by the standard deviation.

Divided the mean by the SD before subtracting. Write the brackets in z = (value − mean) ÷ SD together.

What to say

Ask: how many SDs is that gap?

Questions parents ask

What is the most common mistake with z-scores and normal probabilities?

Flipped the sign of a z-score: a value below the mean has a negative z. Point to the value on a drawn curve together and say which side it is on.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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