Question

Exercise from Biostatistics with R

5.10 Exercises

Make sure to show work/code used in R studio

4 ( b – e)  For part b, ignore the phrase “of each distribution

Consider N(3,2.1) distribution. Do the following tasks:

1. (a) Plot the probability density function and cumulative distribution function.

2. (b) Write down the mean and standard deviation of each distribution.

3. (c) Find the lower tail probability of 4.

4. (d) What is the probability that the value of the random variable is 2?

5. (e) What is the probability that the value of the random variable is bigger than 2 and less than or equal to 4?

10 (only answer the first question)

If the height (in inches) of newborn babies has the N(18,1) distribution, what is the probability that the height of a newborn baby is between 17 and 20 inches? What is the distribution of height in centimeters (1 inch = 2.54 cm)? Using this distribution, what is the probability that the height of a newborn baby is between 43.18 cm (17 inches) and 50.80 cm (20 inches)?

Answer 1

On R.H.S. is output and on L.H..S. is code

RR Graphics: Device 2 ACTIVE) RR Console 0.8 pdf 0.10 cdf 0.4 0.00 > x=rnorm (100,3,2.1); > plot (density (x)) > par (mfrow=c(1,2)) > # probability density function > curve (dnorm (x, 3,2.1), -10, 12,xlab="x", ylab="pdf") > # cumulative distribution function > curve (pnorm(x, 3,2.1), -10,12,xlab="x", ylab="cdf") > # mean and standard deviation of distribution. > mean (x) ; sd (x) [1] 2.738029 [1] 2.08063 > #lower tail probability of 4. TTTTT > pnorm (4, mean = 3, sd =2.1, lower.tail= TRUE) [1] 0.6830307 -10 -5 0 5 10 1 -10 -5 0 5 10 > # the probability that the value of the random variable is 2 > which (x==2) integer (0) Untitled - R Editor > #the probability that the value of the rando > pnorm (4, mean = 3, sd =2.1, lower.tail= TRU x=rnorm (100,3,2.1); [1] 0.3660613 plot (density (x)) par (mfrow=c(1,2)) # probability density function curve (dnorm(x, 3,2.1), -10,12,xlab="x", ylab="pdf") # cumulative distribution function curve (pnorm(x, 3,2.1), -10,12,xlab="x", ylab="cdf") # mean and standard deviation of distribution. mean (x) ; sd (x) #lower tail probability of 4. pnorm (4, mean = 3, sd =2.1, lower.tail= TRUE) # the probability that the value of the random variable is 2 which (x==2) #the probability that the value of the random variable is bigger than 2 and less than or equal to 4 pnorm(4, mean = 3, sd =2.1, lower. tail= TRUE) -pnorm (2, mean = 3, sd =2.1, lower. tail= TRUE)