Answer: a) Mean = [tex]=37.80[/tex]
Standard deviation=[tex]=1.9442[/tex]
b) Mean = [tex]56.00[/tex]
Standard deviation=[tex]4.0988[/tex]
c) Mean = [tex]=24[/tex]
Standard deviation=[tex]2.4495[/tex]
Step-by-step explanation:
To compute Mean and standard deviation , we use following formula:
Mean = [tex]n\pi[/tex]
Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]
a. [tex]n=42,\ \pi=0.90[/tex]
Mean = [tex]42\times0.90=37.80[/tex]
Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]
b. [tex]n=80,\ \pi=0.70[/tex]
Mean = [tex]80\times0.70=56.00[/tex]
Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]
c. [tex]n=32,\ \pi=0.75[/tex]
Mean = [tex]32\times0.75=24[/tex]
Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]
