Exploring Density Curves and the Standard Normal Distribution

What is one of the main objectives of the lesson on density curves and the standard normal distribution?

• To understand the concept of skewness in data

• To learn how to calculate the mode of a data set

• To estimate the relative locations of the median and mean on a density curve

• To learn how to create a pie chart

What is the first step in exploring data from a single quantitative variable?

• Identify outliers

• Calculate the standard deviation

• Plot the data

• Calculate the mean

What does the area under the curve in a histogram represent?

• The relative frequencies or proportions of the observations

• The standard deviation of the data set

• The total number of observations

• The mean of the data set

What is a density curve?

• A curve that always has an area of exactly one underneath it

• A curve that represents the mean of a data set

• A curve that is always symmetric

• A curve that is always below the horizontal axis

What symbol is used to represent the mean of a density curve?

• x̄

• σ

• s

• μ

What is a normal distribution?

• A distribution that has multiple peaks

• A distribution that is symmetric, single-peaked, and bell-shaped

• A distribution that is always skewed to the right

• A distribution that is always skewed to the left

Why are normal distributions important in statistics?

• They are used to calculate the mode

• They are always symmetric

• They are good descriptions of real data and chance outcomes

• They are always skewed

What does the 68-95-99.7 rule state?

• 99.7% of observations fall within three standard deviations of the mean

• 68% of observations fall within three standard deviations of the mean

• 68% of observations fall within two standard deviations of the mean

• 95% of observations fall within one standard deviation of the mean

How do you find the area to the left of a z-score using the standard normal table?

• Locate the z-score in the left-hand column and find the corresponding area in the top row

• Subtract the z-score from 1

• Locate the z-score in the top row and find the corresponding area in the left-hand column

• Add the z-score to 1

What is the syntax for using the normalcdf command on a calculator?

• normalcdf(lower bound, upper bound, mean, standard deviation)

• normalcdf(mean, standard deviation, lower bound, upper bound)

• normalcdf(upper bound, lower bound, mean, standard deviation)

• normalcdf(mean, lower bound, upper bound, standard deviation)