aliens <- read.csv ("aliens.csv", header = TRUE, stringsAsFactors = TRUE)
pnorm(8, mean = 11, sd = 2)
## [1] 0.0668072

##Question 1

pnorm(75, mean= 100, sd=15)
## [1] 0.04779035
pnorm(120, mean =100, sd=15)
## [1] 0.9087888

The probability that a randomly selected person who takes the IQ test would get a score lower than 75 is .04779035. In theory, if this was turned into a percentage it would be around 4%. It is kind of unlikely that an individual will score below 75, so most should be able to score higher than that. The probability that a randomly selected person scores lower than 120 is .9087888. If that was turned into a percentage it would be about 90%. It becomes very likely that someone will score below 120 because 120 is an extremely high IQ level, which would mean that about 90% of people would score below it. The probability reflects this outcome. ##Question 2

1-pnorm(75, mean=100, sd=15)
## [1] 0.9522096
1-pnorm(120, mean=100, sd=15)
## [1] 0.09121122

##Question 3

pnorm(120, mean=100, sd=15)
## [1] 0.9087888
pnorm(140, mean=100, sd=15)
## [1] 0.9961696
.9961696-.9087888
## [1] 0.0873808

I first had to find the probability of an individual getting a score of 120 or lower which is represented in question one. The answer came to 0.9087888 while the probability of someone getting a score of 120 or lower, while doing the same equation which results in 0.9961696. After finding those results, I subtracted those two numbers so that we figure out the space in between them which equals to .0873808.

##Question 4

qnorm(0.9, mean=100, sd=15)
## [1] 119.2233
qnorm(0.8, mean= 100, sd=15)
## [1] 112.6243

##Question 5

(140-100)/15
## [1] 2.666667

The z score associated with an IQ of 140 would be 2.666667 or 7/3.

(95-100)/15
## [1] -0.3333333

The z score associated with an IQ of 140 would be -0.3333333 or -1/3.

##Question 6

IQ <- seq(50, 150, 1)
plot(IQ, dnorm(IQ, 1020, 15), type = "l")

plot(IQ, dnorm(IQ, 100,  10), type ="l")

plot(IQ, dnorm(IQ, 120, 10), type ="l")

##Question 7

hist(aliens$intelligence)

The variable does seem to be normally distributed.

mean(aliens$intelligence)
## [1] 108.5385

The mean for the aliens is slightly higher than the human mean of 100.

sd(aliens$intelligence)
## [1] 9.477959

The standard deviation for aliens is a little less than human standard deviation which would be 15.

Question 8

pnorm(120, mean= 108.5385, sd= 9.477959)
## [1] 0.8867222
(120-108.5385)/9.477959
## [1] 1.209279

An alien would appear to be smarter since 90% of the human population has an IQ less than 120, when the alien population 88.67222 percent have an IQ less than 120, there are more aliens over 120 that is about 2%.

##Question 9

(126-100)/15
## [1] 1.733333
(169-100)/15
## [1] 4.6
pnorm(115, mean= 100, sd=15)
## [1] 0.8413447
pnorm(160, mean= 100, sd=15)
## [1] 0.9999683
pnorm(124, mean= 100, sd=15)
## [1] 0.9452007
pnorm(169, mean=100, sd= 15)
## [1] 0.9999979

Marty scored 115

115
## [1] 115
115+9
## [1] 124