Let X be a random variable with a normal distribution with m

Let X be a random variable with a normal distribution with mean mu = 10 and a standard deviation sigma = 2.5. Write the R script necessary to find the the following probabilities P(X x_0) = 0.9; P(X > x_0) = 0.25; P(|X - 10|

Solution

(a)R-code-

qnorm(0.9,10,2.5)

(b)P(X>x₀)=1-P(X<=x₀)

P(X<=x₀)=1-0.25=0.75

R-code-

qnorm(0.75,10,2.5)

(c)

P(|X-10|<x₀)=P(-x₀<X-10<x₀)=P(X-10<x₀)-P(X-10<-x₀)=P(X-10<x₀)-P(X-10>x₀)=P(X-10<x₀)-{1-P(X-10<x₀)}

=2P(X-10<x₀)-1=0.88

=>P(X-10<x₀)=0.94

R-code-

qnorm(0.94,0,2.5)