1-pnorm(1.2)
## [1] 0.1150697
pnorm(0.53)
## [1] 0.701944
se <- 15000/sqrt(200)
qnorm(.025)*se + 50000
## [1] 47921.14
qnorm(.975)*se + 50000
## [1] 52078.86
# 47921.14 to 52078.86
# From a sample of 200 professionals with population mean 50,000 and standard deviation 15,000, there is a 95% chance that the sample mean will be between 47921.14 and 52078.86
\[ \hat{p} \sim N\left(p,\sqrt{\frac{p(1-p)}{n}}\right)\]
(Using a table) The true proportion of red skittles made at the factory is \(35 \%\). From a sample of \(100\) skittles, what is the probability that the proportion of skittles will be greater than \(40 \%\)?
(Using a table) The true proportion of red skittles made at the factory is \(35 \%\). From a sample of \(100\) skittles, you are really hoping to get an unusually large number of red skittles. What proportion of red skittles would be in the top \(1 \%\) of samples.
Find the middle \(95 \%\)
\[ \mu - 1.96 \cdot SE \leq \bar{X} \leq \mu + 1.96 \cdot SE \]