z-Scores & Normal Distribution

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What is a z-score?

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A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation.

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How do you calculate a z-score?

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The formula for calculating a z-score is: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What does a positive z-score indicate?

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A positive z-score indicates that the value is above the mean.

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What does a negative z-score indicate?

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A negative z-score indicates that the value is below the mean.

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What is the mean height of US women according to the National Health Survey in 2016?

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The mean height of US women in 2016 was 63.6 inches.

Tags

CCSS.6.SP.B.5C

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What is the standard deviation of height for US women according to the National Health Survey in 2016?

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The standard deviation of height for US women in 2016 was 3.11 inches.

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What is the probability of a survey participant being between 61 and 64 inches tall?

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The probability is approximately 0.3512 or 35.12%.

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CCSS.HSS.ID.A.4

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How do you find the probability of a range in a normal distribution?

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To find the probability of a range, calculate the z-scores for the endpoints of the range and then use the standard normal distribution table to find the probabilities.

Tags

CCSS.HSS.ID.A.4

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What is the probability of a survey participant being more than 65 inches tall?

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The probability is approximately 0.3264 or 32.64%.

Tags

CCSS.HSS.ID.A.4

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What is the probability of a survey participant being less than 62 inches tall?

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The probability is approximately 0.3050 or 30.50%.

Tags

CCSS.HSS.ID.A.4