Answer:
Correct: Third option μx = 9 and σx = 2.51
Step-by-step explanation:
Binomial Distribution
Being p the probability of success of an individual event, q the probability of failure (q=1-p) and n the number of independent trials of that event, the expected value or mean of the distribution is
[tex]\mu_x=np[/tex]
And the variance is
[tex]\sigma_x ^2=npq[/tex]
The standard deviation is
[tex]\sigma_x=\sqrt{npq}[/tex]
The given binomial distribution has the following parameters
n = 30, p = 0.3, q = 1 - 0.3 = 0.7. The mean is
[tex]\mu_x=(30)(0.3)=9[/tex]
The standard deviation is
[tex]\sigma_x=\sqrt{(30)(0.3)(0.7)}=\sqrt{6.3}[/tex]
[tex]\sigma_x=2.51[/tex]
The third option is the correct one
