Common Core HSS.ID.A.4 worksheet

Question 1

Adult heights are normally distributed with mean 181 cm and standard deviation 11 cm. Find P(height > 186 cm) to 3 decimal places.

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Question 2

A factory fills 200 bottles. Volumes are normally distributed with mean 412 ml and standard deviation 45 ml. About how many bottles hold more than 457 ml?

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Question 3

A variable is normally distributed with mean 68 and standard deviation 12. About what percentage of values lie between 32 and 104?

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Question 4

A test has mean 52 and standard deviation 3. Find the z-score of a mark of 56.5.

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Question 5

Battery life is normally distributed with mean 252 minutes and standard deviation 33 minutes. Find the probability that a battery lasts between 204 and 256 minutes, to 3 decimal places.

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Question 6

Heights have mean 152 cm and standard deviation 4 cm. What height has a z-score of 1?

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Question 7

Chloe scored 77 in maths (mean 60, sd 10) and 62 in science (mean 56, sd 12). Relative to the class, which was the better result?

• A. Maths
• B. Science

Question 8

A quantity is normally distributed with mean 77 and standard deviation 9. What percentage of values lie between 86 and 95?

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Question 9

Scores have mean 88 and standard deviation 7. What is the z-score of 98.5?

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Question 10

X is normally distributed with mean 103 and standard deviation 14. Find P(X < 103) to 3 decimal places.

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Question 11

Adult heights are normally distributed with mean 182 cm and standard deviation 5 cm. Find P(height > 204 cm) to 3 decimal places.

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Question 12

A factory fills 800 bottles. Volumes are normally distributed with mean 490 ml and standard deviation 38 ml. About how many bottles hold more than 566 ml?

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Question 13

A variable is normally distributed with mean 115 and standard deviation 13. About what percentage of values lie between 89 and 141?

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Question 14

A test has mean 68 and standard deviation 9. Find the z-score of a mark of 54.5.

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Question 15

Battery life is normally distributed with mean 297 minutes and standard deviation 19 minutes. Find the probability that a battery lasts between 280 and 308 minutes, to 3 decimal places.

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Question 16

Heights have mean 170 cm and standard deviation 4 cm. What height has a z-score of −1.5?

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