Answer
a. mean=$75$, variance=$18.75$, standard deviation=$4.33$
b. mean=$90$, variance=$63$, standard deviation=$7.94$
c. mean=$10$, variance=$5$, standard deviation=$2.24$
d. condition does not meet.
Work Step by Step
a. $n=100, p=0.75, q=0.25, np=75, nq=25$
mean=$np=75$
variance=$npq=18.75$
standard deviation=$\sqrt {npq}=4.33$
b. $n=300, p=0.3, q=0.7, np=90, nq=210$
mean=$np=90$
variance=$npq=63$
standard deviation=$\sqrt {npq}=7.94$
c. $n=20, p=0.5,q=0.5, np=10, nq=10$
mean=$np=10$
variance=$npq=5$
standard deviation=$\sqrt {npq}=2.24$
d. $n=10, p=0.8, q=0.2, np=8, nq=2\lt5$
condition does not meet.
