chapter 13-14 statistical inference

Author

Rachel Saidi

Chapter 13 - Mathematical Modeling with Normal Distribution Calculations

Example2:

Head lengths of brushtail possums follow a nearly normal distribution with mean 92.6 mm and standard deviation 3.6 mm.

  1. Compute the Z scores for possums with head lengths of 95.4 mm and 85.8 mm.
  2. A brushtail possum is found to have a head length of 85.8 mm. What percentile of possums have head lengths 85.8 mm or smaller?
  3. A brushtail possum is found to have a head length of 95.4 mm. What percentile of possums have head lengths 95.4 mm or more?
# Answers 
#a
(95.4-92.6)/3.6
[1] 0.7777778
#b
pnorm(85.8, mean = 92.6, sd = 3.6)
[1] 0.02945336
#c
1 - pnorm(95.4, mean = 92.6, sd = 3.6)
[1] 0.21835
#c (alternative code)
pnorm(95.4, mean = 92.6, sd = 3.6, lower.tail = FALSE)
[1] 0.21835

To draw the pictures of these areas, use this code:

#b drawing
openintro::normTail(m = 92.6, s = 3.6, L = 85.8) 

     # notice L is used to shade the lower tail

#c drawing
openintro::normTail(m = 92.6, s = 3.6, U = 95.4)

      # notice U is used to shade the upper tail

Example3:

Head lengths of brushtail possums follow a nearly normal distribution with mean 92.6 mm and standard deviation 3.6 mm.

  1. What possum head length is in the bottom 20th percentile?
  2. What head length is in the top 5th percentile?
# Answers: (note p must be a percentile, which means it represents area to the left of the cutoff)
#a
qnorm(p=.20, m=92.6, s=3.6) 
[1] 89.57016
#b
qnorm(p=.95, m=92.6, s=3.6)
[1] 98.52147