Given a random variable, x that arises from a binomial experiment and suppose that n = 10, and p = 0.81.
PART A:
The probability distribution for a binomial experiment is given as
[tex]\begin{gathered} b\mleft(x;n,p\mright)=^nC_xp^{x(}(1-p)^{n-x} \\ b(x;n,p)=^nC_xp^{x(}(q)^{n-x} \\ b(x;n,p)=^{10}C_x(0.81^x)(0.19)^{10-x} \end{gathered}[/tex]where q =1-p
PART B
One way to illustrate the binomial distribution is with a histogram. A histogram shows the possible values of a probability distribution as a series of vertical bars. The height of each bar reflects the probability of each value occurring.
The histogram is given below:
PART C
The shape of the histogram shows it is skewed to the left.
PART D.
The mean of a binomial experiment is given below:
[tex]\begin{gathered} \mu=n\times p \\ \mu=10\times0.81 \\ \mu=8.1 \end{gathered}[/tex]PART E
The variance of a binomial experiment is
[tex]\begin{gathered} \text{Variance= n x p x q} \\ =10\times0.81\times0.19 \\ =1.539 \end{gathered}[/tex]PART F
The standard deviation is the square root of the variance.
[tex]\begin{gathered} sd=\sqrt[]{\text{variance}} \\ sd=\sqrt[]{1.539} \\ s\mathrm{}d=1.241 \end{gathered}[/tex]
