---
title: "PSY 392 - HW2"
output: html_document
---
Please read everything carefully!!!

*** Due Friday, September 13th at 5:00 PM via email to Garrett (goday@purdue.edu)

*** Submit this R markdown file but change the name of the file to lastName_FirstName_PSY392_HW2

Rmarkdown:
This document is a R markdown file and has the file extension ".rmd".

"R Markdown is a file format for making dynamic documents with R. An R Markdown document is written in markdown (an easy-to-write plain text format) and contains chunks of embedded R code, like the document below."

To add code you can click on 'Code' in the top menu bar and select 'Insert Chunk'. 
Alternatively, you can type '''{r} to start a code chunk and ``` to close a code chunk.

```{r}
# this is an example code chunk. 
# Anything between lines 16 and 18 is considered code.
2+2
```

Rmarkdown has three major benefits for this class:
1) I do not have to use comments outside of a code chunk, making the document more readable.
2) The output of a code chunk is presented below it, This allows me to see your exact output.
3) Please write all of your answers within a code chunk. This makes grading easier.



Homework Overview:
The purpose of this homework is to continue supporting your learning of R, expose you to Rmarkdown, and provide an opportunity for you to use and apply your knowledge about the normal distribution. 

Question 1.
What are the unique characteristics of the standard normal distribution?
```{r}
# provide your answer as a comment in this code chunk


```

The online calculators will help you with this homework.

The Normal Distribution Calculator (https://introstatsonline.com/chapters/calculators/normal_dist.shtml) 

The Inverse Normal Distribution Calculator (https://introstatsonline.com/chapters/calculators/inverse_normal_dist.shtml)

Question 2.
We know that for a standard normal distribution, the shaded area above 0 is .5. 
How does increasing the standard deviation affect the shaded area above 0?
```{r}
# provide your answer as a comment in this code chunk


```


Question 3.
For a standard normal distribution, what is the area between -1 and 1 SDs?
```{r}
# provide your answer as a comment in this code chunk


```

Question 4.
Suppose that a intro to chemistry class has 500 students.
They all take a midterm and their scores are normally distributed.
The professor says anyone who scores 1.75 standard deviations above the mean will get an A.
How many students will receive an A on their midterm? (note the unit of interest)
```{r}
# provide your work in this code chunk


```

Question 5.
Suppose you have a normal distribution with a mean of 75 and a standard deviation of 15.
What percentile corresponds to a score of 100?
```{r}
# provide your work and/or explain your reasoning in this code chunk


```



Answer questions 6-10 using information from the following scenario.

A psychology professor graded a midterm for a class of 100 students on strict cut offs of:
90 - 100% = A
80 - 89.9% = B
70 - 79.9% = C
60 - 69.9% = D
< 60% = F

Imagine that the actual test scores were normally distributed. With a mean of 85% and a standard deviation of 10%.

Question 6.
How many students received an A?
```{r}
# provide your answer as a comment in this code chunk
# be sure to explain your reasoning


```

Question 7.
How many students received a B?
```{r}
# provide your answer as a comment in this code chunk
# be sure to explain your reasoning


```

Question 8.
How many students received a C?
```{r}
# provide your answer as a comment in this code chunk
# be sure to explain your reasoning


```

Question 9.
How many students received a D?
```{r}
# provide your answer as a comment in this code chunk
# be sure to explain your reasoning


```

Question 10.
How many students failed the midterm?
```{r}
# provide your answer as a comment in this code chunk
# be sure to explain your reasoning


```

Question 11 - Computing Z scores in R.
R comes with a number of built in data sets that people can explore.
When people ask for help online, people often provide answers using these universal data frames since every user has them.
For question 13, you will compute and plot z scores for the mtcars data frame.

```{r}
# create a dataframe (df) to contain mtcars
carsData <- mtcars
head(carsData) # peek at the first 6 rows of this data frame
carsData$mpg   # look at mpg column

# a) compute the mean mpg

# b) compute the sd mpg

# c) create a new column in the data frame that converts each mpg value into a z score

# d) what are the units of this new column?

# e) what is the mean of this new column?

# f) what is the standard deviation of this new column?

# g) create a visualization of the z score column

# h) provide a brief description of your visualization

```