knitr::opts_chunk$set(message = FALSE, results="show", echo = TRUE)
library(tigerstats)

Question 3.7 - L.A. Weather, Part 1

The average daily high temperatures in June in LA is 77°F with a standard deviation of 5°F. Suppose that the temperatures in June closely follow a normal distribution.

Part a

What is the probability of observing an 83°F temperature or higher in LA during a randomly chosen day in June?

\(Z=\frac{ x - \mu}{\sigma}\)

z_a <- (83 - 77) / 5
print(z_a)
## [1] 1.2
pnormGC(83, region="above", mean=77,
        sd=5,graph=TRUE)

## [1] 0.1150697

Part b

How cold are the coldest 10% of days during June in LA?

qnorm(0.10, mean = 77, sd = 5)
## [1] 70.59224
pnormGC(70.6, region="below", mean=77,
        sd=5,graph=TRUE)

## [1] 0.1002726