Algebra 2 9.8 Normal Distributions

Front

What does the z-score represent?

Back

The amount of standard deviations a data value is above or below the mean.

Front

What is the total area under the standard normal distribution curve?

Back

1

Front

What IQ level qualifies one to be a member of Mensa, given a normal distribution with μ=100 and 𝞂=15?

Back

130.75

Front

If a male long jumper's jump ranked in the 75th percentile, how long was his jump if the mean is 263 inches and the standard deviation is 14 inches?

Back

272.38 inches

Front

What proportion of teenagers have waist sizes greater than 31 inches if the average waist size is 29 inches with a standard deviation of 1.4 inches?

Back

7.6%.

Front

Define normal distribution.

Back

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the mean in a normal distribution?

Back

The average value of a set of data, which is the center of the normal distribution.

Front

What is the standard deviation in a normal distribution?

Back

A measure of the amount of variation or dispersion of a set of values.

Front

What does the 68-95-99.7 rule state?

Back

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

How do you calculate a z-score?

Back

Z = (X - μ) / 𝞂, where X is the value, μ is the mean, and 𝞂 is the standard deviation.