Normal Distribution: Fresh Take

  • Understand the properties, characteristics, and importance of a normal distribution in statistical analysis.
  • Explain how changing the mean and standard deviation will change the characteristics of a normal curve.

Recall that a normal distribution is a mathematical model with a smooth bell-shaped curve.

The final exam scores in a statistics class were normally distributed with a mean of [latex]63[/latex]and a standard deviation of five.A normal distribution curve with boxes marked A, B, C, D, E, F, G corresponding to ticks on the x-axis.
(a) What is the value of each tick mark labeled above?

(b) The score of ______ is [latex]1[/latex] standard deviation above the mean.

(c) The score of ______ has a [latex]z[/latex]-score of [latex]-3[/latex].

Find the mean and standard deviation of the following curves.A normal curve in black with a mean of 10, a curve in red with a mean of 10, and a curve in green with a mean of 14.(a) What is the mean and standard deviation of the black color normal distribution curve?

(b) What is the mean and standard deviation of the red color normal distribution curve?

(c) What is the mean and standard deviation of the green color normal distribution curve?