Central Limit Theorem and Normal Distributions

UNG MATH 3350 (online)

I. Initializing Block

Initializing RStudio

The Mosaic package was created by statistics instructors to help students learn the coding in R. Commands are streamlined to be more intuitive. Execute the code block below to load Mosaic (required each session).

library(mosaic)

II. Exercises

1. Find the percentile ranking for an IQ score of 120 using the xpnorm function. IQ’s have the \(N(100,15)\) distribution.

2. Find the approximate IQ score that corresponds to the 25th percentile IQ. Use the xqnorm function. IQ’s have the \(N(100,15)\) distribution.

3. Find the percentile ranking for an SAT-Math score of 700 using the xpnorm function. SAT components have the \(N(500,100)\) distribution.

4. Find the approximate SAT-Math score that corresponds to the 60th percentile SAT-Math score. Use the xqnorm function. SAT components have the \(N(500,100)\) distribution.

5. Find the “middle 90%” of the IQ distribution. The middle 90% will be a symmetric interval that traps exactly 5% of the area below it, 5% above it, and thus 90% within it. Use the xqnorm function. IQ components have the \(N(100,15)\) distribution.

III. Code Blocks

coins = do(50) * rflip(20)
histogram(~heads, data = coins,
          width = 1,
          fit = "normal")

coins = do(200) * rflip(20)
histogram(~heads, data = coins,
          width = 1,
          fit = "normal")

coins = do(1000) * rflip(20)
histogram(~heads, data = coins,
          width = 1,
          fit = "normal")

xpnorm(29,21,6)

xpnorm(1.333)

xqnorm(.45,21,6)