UI STAT 251 Fall 2010 Quiz 3 NAME:
KEY
UI #:
Class: 9:30 / 10:30 (circle yours)
1. If you can choose 4 numbers between -10 to 10 with repeats so that you obtain the largest standard deviation,
how would you choose the four numbers? What are they? What is the resulting standard deviation?
The numbers are -10, -10, 10, 10 and the maximum sd is:
> sd(c(-10,-10,10,10))
[1] 11.54701
2. IQ tests are standardized to a Normal model with a population mean of 100 and a population standard deviation
of 20.
a) What percent of people should have IQ scores between 108 and 118?
> pnorm(118, mean=100, sd=20)- pnorm(108, mean=100, sd=20)
[1] 0.1605181
b) What is the highest 5% of all IQs?
> qnorm(.95,mean=100,sd=20)
[1] 132.8971
c) What is the Inter-Quartile Range of the IQs?
> qnorm(.75,mean=100,sd=20)-qnorm(.25,mean=100,sd=20)
[1] 26.97959
d) What is the 44-percetile of the IQ score?
> qnorm(.44,mean=100,sd=20)
[1] 96.98062
3. In R, consider the data set faithful$waiting.
a) What is the mean and standard deviation of these waiting times?
> mean(faithful$waiting)
[1] 70.89706 minutes
> sd(faithful$waiting)
[1] 13.59497 minutes
b) What is the 62-percentile of these waiting times?
> quantile(faithful$waiting,.62)
62%
78 minutes
c) What proportion of these waiting times is longer than 80 minutes?
> sum(faithful$waiting>80)/272
[1] 0.3088235
d) What proportion of these waiting times is shorter than half standard deviation below the mean?
> sum(faithful$waiting<(70.89706-13.59497/2))/272
[1] 0.3455882