Finding the Area/Probability Under a Normal Curve

Front

What is the area under the normal distribution curve to the left of Z=0.27?

Back

0.6064

Front

What is a normal distribution curve?

Back

A normal distribution curve is a bell-shaped curve that represents the distribution of a continuous random variable, characterized by its mean and standard deviation.

Front

What is the area under the standard normal curve to the right of z = -2.67?

Back

0.9962

Front

How do you calculate a Z-score?

Back

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

Front

If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?

Back

+1.25

Front

What does a Z-score represent?

Back

A Z-score indicates how many standard deviations an element is from the mean.

Front

What is the total area under a normal distribution curve?

Back

1 (or 100%)

Front

What is the significance of the area under the curve in probability?

Back

The area under the curve represents the probability of a random variable falling within a particular range.

Front

What is the empirical rule in relation to normal distribution?

Back

Approximately 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Front

What is the standard normal distribution?

Back

A normal distribution with a mean of 0 and a standard deviation of 1.