Question

A-. Consider the data set {1,2,4,5,7,8,9,9,10,1,12,11,14,16,17,20,22,23,25,27,35}

1. Construct a Box Plot.
2. Upload the document with the box plot.

B-.GPAs at CCSU are normally distributed with a mean of 2.38 and a standard deviation of 0.45. Find the z-score for a GPA of 3.06. and discuss the significance of the z-score.

Answer 1

SolutionA:

use R software .boxplot function to get the boxplot.

Rcode;

sample <- c(1,2,4,5,7,8,9,9,10,1,12,11,14,16,17,20,22,23,25,27,35)
boxplot(sample,main="boxplot", col = "pink")
fivenum(sample)
abline(h = min(sample), col = "Blue",horizontal = TRUE)
abline(h = max(sample), col = "Yellow")
abline(h = median(sample), col = "Green")

Output:

Fivenum summary from boxplot is

minimum value=1

first quartile=Q1=7

second quartile=Q2=11

third quartile=Q3=20

maximum value=35

B-.GPAs at CCSU are normally distributed with a mean of 2.38 and a standard deviation of 0.45.

Z score=x-mean/stddeviation

=3.06-2.38/0.45

=0.68/0.45

=1.511111

z score for GPA=3.06 is 1.511111

it means it lies 1.51111 standard deviations away from mean.