Question 1

The temperatures (in \(^\circ\text{F}\)) recorded at Exton at noon on each day for two weeks in July are below. Use the results from this sample to estimate the population mean and standard deviation.

\[\text{Temps} = [81,78,77,75,80,82,84,78,74,75,49,71,76,77]\]

Temps <- c(81,78,77,75,80,82,84,78,74,75,49,71,76,77)
cat("The population mean is:",mean(Temps),"\n")
## The population mean is: 75.5
cat("The standard deviation is:",sd(Temps),"\n")
## The standard deviation is: 8.3551

Question 2

Express 0.714285714285 as a fraction.

# install.packages("MASS")
library(MASS)
fractions(0.714285714285)
## [1] 5/7

Question 3

What is \(\frac{d}{dz} (z^3 - 3z^2)\)?

# install.packages("Deriv")
library(Deriv)
f <- function(z) {
  z^3 - 3 * z^2
}
f_prime <- Deriv(f)
f_prime
## function (z) 
## z * (2 * (z - 3) + z)