Question

Cut and paste into Word... Your Problem IV: Generating and Displaying Continuous data: rnorm( n, μ,0) In 2014 a large study of 435 college graduates found the number of years it takes to complete a bachelors (first time) was normally distributed w mean 5.4 years and sd .3 [1] Generate n-100 random normally distributed variables N ( ,0 ) N (5.4 , .3) Call it bachelors. [21 Using par function, plot both hist(bachelors) and boxplot(bachelors) and compare the two graphs 13] Find the mean(bachelors), call it xbar. Also find the sd(bachelors), call it s.norm. How closely are xbar and s.norm to the given 5.4 and .3 [4] Find the summary statistics using: summary(bachelors) and comment on mean and sd of the randomly generated data.

> summary(bachelors)
Min. 1st Qu. Median Mean 3rd Qu. Max.
4.640 5.231 5.395 5.434 5.637 6.040

How to comment on mean and sd of the randomly generated data?

Answer 1

Attached are the codes

# To generate 100 random normal distributions
bachelors <- rnorm(100, mean = 5.4, sd = 0.3)
par(par(mfrow=c(2,2)))
hist(bachelors)
boxplot(bachelors)
x_bar <- mean(bachelors)
s.norm <- sd(bachelors)
print(x_bar)
print(s.norm)
x_bar = 5.403714

sd = 0.3175386

summary(bachelors)
Min. 1st Qu. Median Mean 3rd Qu. Max.
4.436 5.192 5.424 5.404 5.600 6.275

Histogram of bachelors CN 12 12 4.5 5.0 5.5 6.0 bachelors

.0 6 5 5 0 5 5 4

RStudio File Edit Code View Plots Session Build Debug Profile Tools Help nction Addins : source on Save Run Source # To generate 100 random normal distributions 2 bachelors rnorm(100, mean-5.4, sd 0.3) 3 par (par(mfrow-c(2,2))) 4 hist (bachelors) 5 boxplot(bachelors) 6 x bar mean (bachelors) 7 s.normsd(bachelors) 8 print(x_bar) 9 print(s.norm) 10 summary (bachelors) 111 Top Level) R Script Console Terminal > print(x_bar) [1] 5.403714 > print (s.norm) [1] 0.3175386 > summary (bachelors) Min. 1st Qu. Median Mean 3rd Qu. Max 4.436 5.192 5.424 5.404 5.600 6.275