Normal Probability Robinson

Front

What is a z-score?

Back

A z-score indicates how many standard deviations a data point is from the mean. It is calculated as (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

How do you calculate the speed of a car given its z-score?

Back

To find the speed, use the formula: Speed = μ + (z * σ). For example, if μ = 23.84 mph and σ = 3.56 mph, and z = 3.2, then Speed = 23.84 + (3.2 * 3.56) = 35.232 mph.

Front

What does the 96th percentile mean in a normal distribution?

Back

The 96th percentile means that 96% of the data points fall below this value. For example, if a baby is in the 96th percentile for height, it is taller than 96% of babies.

Front

What is the mean and standard deviation of human pregnancies?

Back

The mean length of human pregnancies is 268 days, and the standard deviation is 15 days.

Front

How do you find the percentage of pregnancies lasting at least 300 days?

Back

Calculate the z-score for 300 days using the formula: z = (X - μ) / σ. Then, use the z-table to find the corresponding percentage.

Front

What is the z-score for a data point that equals the mean?

Back

The z-score for a data point that equals the mean is 0.

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the total probability, which equals 1. Specific areas correspond to probabilities of certain outcomes.

Front

How do you interpret a standard deviation in a normal distribution?

Back

Standard deviation measures the dispersion of data points from the mean. A smaller standard deviation indicates that data points are closer to the mean.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Front

How do you calculate the percentage of ratings between two values in a normal distribution?

Back

Find the z-scores for both values, then use the z-table to find the area between those z-scores to determine the percentage.