Learning Target 12.3 Standard Scores (z-scores)

In a normal distribution, a data value located 2.1 standard deviations below the mean has what standard z score?

• -2.1

• 2.1

• 0

• 1

The weights of a certain dog breed are approximately normally distributed with a mean of 45 pounds and a standard deviation of 4 pounds. A dog of this breed weighs 54 pounds. What is the dog’s z-score?

• 1.5

• 2.25

• 2.5

• 3

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CCSS.HSS.ID.A.4

The weights of a certain dog breed are approximately normally distributed with a mean of 45 pounds and a standard deviation of 4 pounds. A dog has a z-score of -2.2. What is the dog’s weight?

• 36.2 pounds

• 36.8 pounds

• 37.2 pounds

• 37.8 pounds

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CCSS.HSS.ID.A.4

The weights of a certain dog breed are approximately normally distributed with a mean of 45 pounds and a standard deviation of 4 pounds. A dog has a z-score of 2.2. What is the dog’s weight?

• 53.8 pounds

• 54.8 pounds

• 55.8 pounds

• 56.8 pounds

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CCSS.HSS.ID.A.4

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If a person has a z-score of 1.4, what is that person’s IQ?

• 121

• 110

• 115

• 120

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CCSS.HSS.ID.A.4

The weights for newborn babies are approximately normally distributed with a mean of 6.1 pounds and a standard deviation of 1.5 pounds. What percentage of babies weigh less than 7 pounds?

• About 60.6%

• About 74.5%

• About 82%

• About 92.1%

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CCSS.HSS.ID.A.4

The weights for newborn babies are approximately normally distributed with a mean of 6.1 pounds and a standard deviation of 1.5 pounds. What percentage of babies weigh more than 5.5 pounds?

• About 26%

• About 70%

• About 50%

• About 80%

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CCSS.HSS.ID.A.4

The weights for newborn babies are approximately normally distributed with a mean of 6.1 pounds and a standard deviation of 1.5 pounds. What percentage of babies weigh between 5 to 7 pounds?

• 34.1%

• 47.8%

• 10%

• 15.9%

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CCSS.HSS.ID.A.4

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly chosen person has an IQ greater than 90?

• 0.2525

• 0.7475

• 0.8413

• 0.1587

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CCSS.HSS.ID.A.4

Assume that SAT scores are normally distributed with a mean of 1000 and a standard deviation of 200. If you earned a 1260 on the SAT, your score was better than what percentage of the students taking that test?

• 84%

• 90%

• 95%

• 97%

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CCSS.HSS.ID.A.4