Problem 3.1 - Area Under the curve, Part 1

What percent of standard normal distribution \[N(\mu=0, \sigma=1)\] is found in each region? Be sure to draw a graph

  1. Z < -1.35

Answer: Percent of Area under curve 8.85%

  1. Z > 1.48

Answer: Percent of Area under curve 1 - .9306 = 6.94%

  1. -0.4 < Z < 1.5

Answer:

Percent of Area under curve for Z less than -0.4 = 34.46%

Percent of Area under curve for Z greater than 1.5 = 1 - 93.32% = 6.68%

So Area under curve for -0.4 < Z < 1.5 = 100% - 34.46% - 6.68% = 58.86%

  1. |Z| > 2

Answer:

Percent of Area under curve for Z less than -2 = 2.28%

Percent of Area under curve for Z greater than 2 = 1 - 97.72% = 2.28%

So Area under curve for | Z | = (2.28%)*2 = 4.56%

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.