The mean of the binomial distribution to the nearest tenth = 4.7
Variance to the nearest tenth = σ²= 1.0
Explanation:
1) The probability = p = 79%
The total number of people in the survey = n = 6
We apply the formula for calculating mean in binomial distribution:
[tex]\operatorname{mean}\text{ = n}\times p[/tex][tex]\begin{gathered} \operatorname{mean}\text{ = 6}\times79\text{ percent} \\ \operatorname{mean}\text{ = 6 }\times0.79 \\ \operatorname{mean}\text{ = 4.7}4 \end{gathered}[/tex]The mean of the binomial distribution to the nearest tenth = 4.7
2) the formula for variance = n*p(1-p)
variance = σ² = 6*0.79(1 - 0.79)
[tex]\begin{gathered} \sigma^{2}=6\times0.79\mleft(1-0.79\mright) \\ \sigma^{2}=4.74(0.21) \\ \sigma^{2}=\text{ 0.9954} \end{gathered}[/tex]Variance of the binomial distribution to the nearest tenth = σ²= 1.0
