Problem I
(a) The data of students heights is approximately normally
distributed
(b) The data of students pulses is approximately normally
distributed
(c) The data of students GPAs is approximately normally
distributed
(d) The proportion of students heights that lies within one standard
deviation away from the mean is 0.735
## [1] 0.735
Problem I
(e) The proportion of students pulses that lies within two standard
deviations away from the mean is 0.96
## [1] 0.96
(f) The proportion of students GPAs that lies within three standard
deviations away from the mean is 0.985
## [1] 0.985
R Code Appendix (will automatically list all code used)
student <- read.csv("student.csv")
qqnorm(student$height,main="Normal Probability Plot for Student's Height")
qqline(student$height)
qqnorm(student$pulse,main="Normal Probability Plot for Student's Pulses")
qqline(student$pulse)
qqnorm(student$hsGPA,main="Normal Probability Plot for Student's GPA")
qqline(student$hsGPA)
X=student$height
the.mean=mean(X)
the.sd=sd(X)
one.sd.away=mean(X<the.mean+the.sd&X>the.mean-the.sd)
one.sd.away
Y=student$pulse
the.mean=mean(Y)
the.sd=sd(Y)
two.sd.away=mean(Y<the.mean+2*the.sd&Y>the.mean-2*the.sd)
two.sd.away
S=student$hsGPA
the.mean=mean(S)
the.sd=sd(S)
three.sd.away=mean(S<the.mean+3*the.sd&S>the.mean-3*the.sd)
three.sd.away