Answer:
(a) [tex]s = 2.56[/tex]
(b) [tex]s = 1.71[/tex]
Step-by-step explanation:
Given
Tables (a) and (b)
Required
Determine the standard deviation
For (a):
[tex]\bar x = 11.5[/tex] --- mean
The standard deviation is calculated as:
[tex]s = \sqrt{\sum np(1-p)}[/tex]
This gives:
[tex]s = \sqrt{5*0.1*(1-0.1) +10 * 0.5 * (1 - 0.5) + 15 *0.4*(1-0.4) }[/tex]
[tex]s = \sqrt{5*0.1*0.9 +10 * 0.5 * 0.5 + 15 *0.4*0.6 }[/tex]
[tex]s = \sqrt{6.55}[/tex]
[tex]s = 2.56[/tex]
For (b):
[tex]\bar x = 4.4[/tex] --- mean
The standard deviation is calculated as:
[tex]s = \sqrt{\sum np(1-p)}[/tex]
This gives:
[tex]s = \sqrt{1*0.2*(1-0.2) +3 * 0.3 * (1 - 0.3) + 5 *0.1*(1-0.1) + 7*0.4*(1-0.4)}[/tex]
[tex]s = \sqrt{1*0.2*0.8 +3 * 0.3 * 0.7 + 5 *0.1*0.9 + 7*0.4*0.6}[/tex]
[tex]s = \sqrt{2.92}[/tex]
[tex]s = 1.71[/tex]
