Stat 3011 Midterm 1 (Computer Part)

Problem 1

(a)

Rweb:> pnorm(0, mean=25, sd=10)
[1] 0.006209665

(b)

Rweb:> pnorm(30, mean=25, sd=10) - pnorm(25, mean=25, sd=10)
[1] 0.1914625

(c)

Rweb:> qnorm(0.90, mean=25, sd=10)
[1] 37.81552

Problem 2

(a)

Rweb:> 1 - pnorm(6.5, mean = 5.31, sd = 0.58) 
[1] 0.02009824

(b)

Rweb:> pnorm(6.5, mean = 5.31, sd = 0.58) 
[1] 0.9799018

(c)

Rweb:> 1 - pnorm(6.5, mean = 11.74, sd = 3.50) 
[1] 0.932822

(d)

Rweb:> pnorm(6.5, mean = 11.74, sd = 3.50) 
[1] 0.06717805

Problem 3

(a)

You want either a histogram or a stem and leaf plot. They show pretty much the same thing. The histogram is just prettier. The R default stem and leaf plot is

Rweb:> "your name here" 
[1] "your name here" 
Rweb:> stem(sally) 
 
  The decimal point is at the | 
 
  -0 | 5 
   0 | 3 
   1 | 16789 
   2 | 111224444566789999 
   3 | 000223333344555555566777789999 
   4 | 0000111122244445555666667778888999 
   5 | 000001111112222333333333444555667777788888899 
   6 | 000111112222333445566778999 
   7 | 0001333333444444555667789 
   8 | 000234579 
   9 | 059 
  10 | 11237 
  11 | 057799 
  12 | 01456679999 
  13 | 13444566679999 
  14 | 00111112334444556666889999 
  15 | 003466889 
  16 | 1223344678899 
  17 | 01245677789 
  18 | 00269 
  19 |  
  20 | 3 
  21 |  
  22 | 6

(b)

Skewed. Long right tail (positive skewness). Bimodal. Maybe the 20.3 and 22.6 are outliers, but this is better described as just the long right tail.

(c)

Rweb:> mean(sally) 
[1] 8.396367

(d)

Rweb:> median(sally) 
[1] 6.39

(e)

Rweb:> sd(sally) 
[1] 5.001011

(f)

Rweb:> IQR(sally) 
[1] 8.8875

(g)

The mean goes with the standard deviation like ham and eggs. Similarly the median goes with the IQR.

Thus one sensible answer is mean (estimate of center) and standard deviation (estimate of spread). And another sensible answer is median (estimate of center) and IQR (estimate of spread). An argument can be made for either of these. No argument can be made for any other answer.

For this particular problem, neither is really satisfactory. A bimodal distribution really has two ``centers'' so no single measure of ``center'' can be satisfactory.