z-Scores & Normal Distribution

Front

What is a z-score?

Back

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.

Front

How do you calculate a z-score?

Back

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.

Front

What does a positive z-score indicate?

Back

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

Front

What does a negative z-score indicate?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The probability is approximately 0.3512 or 35.12%.

Front

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

Back

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.

Front

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

Back

The probability is approximately 0.3264 or 32.64%.

Front

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

Back

The probability is approximately 0.3050 or 30.50%.