Given X find Area of Normal Curve

Front

What is the mean in a normal distribution?

Back

The mean is the average value of a set of data points, representing the center of the distribution.

Front

What shape is a normal distribution curve?

Back

The normal distribution curve is shaped like a bell, known as the bell curve.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion in a set of values.

Front

If a continuous random variable is normally distributed with mean 145 and standard deviation 5, what is P(136

Back

P(136

Front

What proportion of weeks would you expect to have less than 5 accidents if the mean is 6.4 and standard deviation is 1.5?

Back

The proportion is 0.1762.

Front

What percent of students have a GPA between 2.9 and 3.8 if the mean GPA is 3.2 and standard deviation is 0.3?

Back

81.5% of students have a GPA between 2.9 and 3.8.

Front

Define a continuous random variable.

Back

A continuous random variable can take any value within a given range, as opposed to discrete variables which can only take specific values.

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 z-score?

Back

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

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean.