Question

USING R SOFTWARE FOR STATISTICAL ANALYSIS: (SHOW YOUR CODE)

Suppose that the current measurements in a strip of wire follow a normal distribution with a mean of 10 mA and a variance of 4 mA². What is the probability that a measurement exceeds 13 mA?

Make an area under the curve graph.

 

Answer 1

Here we have

Since area under the normal curve lies within 4 SDs of mean so we need to area between 13 and .

Following is the R-script to find the required probability:

# Assigning values to variable
mean=10; sd=2
lb = 13; ub=18

# Generating sequence of numbers between 2 and 18 of length 100

x <- seq(-4,4,length=100)*sd + mean

# Creating normal curve

hx <- dnorm(x,mean,sd)

plot(x, hx, type="n", xlab="IQ Values", ylab="",
main="Normal Distribution", axes=FALSE)

axis(1, at=seq(2, 18, 2), pos=0)
i <- x >= lb & x <= ub
lines(x, hx)

# SHowing area corresponding to required probability

polygon(c(lb,x[i],ub), c(0,hx[i],0), col="grey")

area <- pnorm(ub, mean, sd) - pnorm(lb, mean, sd)
result <- paste("P(",lb,"< IQ <",ub,") =",
signif(area, digits=3))
mtext(result,3)

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Following is the screen shot of curve:

Following is the screen shot of code:

Answer: 0.0668