Let X be a random variable normally distributed with parameters
\(\mu\) = 70 and \(\sigma\) = 10 Estimate: (a) P(X > 50)
We calculate the standard normal variable as follows: \(Z=\frac{Y-\mu}{\sigma}\) P(X>50)=P(Z>50-70/10)=P(Z>-2)=1-P(Z<-2)
1-pnorm(-2,0,1)
## [1] 0.9772499
- P(X < 60) We calculate the standard normal variable as follows: \(Z=\frac{Y-\mu}{\sigma}\) P(X<60)=P(Z<60-70/10)=P(Z<-1)
pnorm(-1,0,1)
## [1] 0.1586553
- P(X > 90) We calculate the standard normal variable as follows: \(Z=\frac{Y-\mu}{\sigma}\) P(X>90)=P(Z>90-70/10)=P(Z>2)=1-P(Z<2)
1-pnorm(2,0,1)
## [1] 0.02275013
- P(60 < X < 80) P(60<X<80) = P(60-70/10<Z<80-70/10)=P(-1<Z<1)
pnorm(1,0,1)-pnorm(-1,0,1)
## [1] 0.6826895