G11 Stat Normal Distribution

What is the shape of a normal distribution curve?

• Skewed to the left

• Skewed to the right

• Symmetrical bell-shaped curve

• U-shaped

Define the mean, median, and mode in the context of a normal distribution.

• Mean = highest point, Median = average value, Mode = center point

• Mean = center point, Median = highest point, Mode = average value

• Mean = average value, Median = center point, Mode = highest point

• Mean = center point, Median = center point, Mode = center point

How does the standard deviation affect the width of a normal distribution curve?

• Higher standard deviation = narrower curve

• Higher standard deviation = wider curve

• Standard deviation does not affect the width

• Standard deviation makes the curve asymmetrical

What percentage of data falls within one standard deviation of the mean in a normal distribution?

• 34%

• 50%

• 68%

• 95%

Explain the concept of z-scores in relation to a normal distribution.

• Measures the spread of data

• Represents the distance from the mean in standard deviations

• Determines the mode of the distribution

• Calculates the median value

Describe the characteristics of a standard normal distribution.

• Mean = 0, Standard Deviation = 1

• Mean = 1, Standard Deviation = 0

• Mean = 0, Standard Deviation = 0

• Mean = 1, Standard Deviation = 1

If a data set is normally distributed, what percentage of data falls below the mean?

• 25%

•  50%

• 68%

• 95%

How do you calculate the area under a normal distribution curve for a given range of values?

• Use the median

• Use the mode

• Use z-scores

• Use integration or lookup tables

What is the empirical rule, and how is it applied in a normal distribution?

• States that 90% of data falls within 2 standard deviations of the mean

• Describes the characteristics of an exponential distribution

• Outlines the percentage of data within 1, 2, and 3 standard deviations from the mean

• Predicts the mode of a distribution

In constructing a normal distribution curve, what are the key components that need to be determined or known?

• Mean and median

• Median and mode

• Mean and standard deviation

• Mode and standard deviation