To find: The probability of getting exactly 14 variegated plants. Given

Calculation:
Define the random variable x as the number of variegated plants. Here, the total numbers of plants (n) are 200 and each plant is independent of another plant.Also, there are two possible outcomes (it is a variegated plant or not a variegated plant) and the probability of that the selected plant which turns out to be a variegated plant gives the probability of success as (p) 0.05. Thus, x follows binomial distribution.
The binomial distribution formula is,
${\displaystyle P\left(x\right)=\frac{n!}{(n-x)!x!}{p}^x{q}^{n-x}}$
Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.
Substitute ${\displaystyle nas200,pas0.05,qas0.95(=1-0.05)}$
Software procedure:
Software procedure for calculating the binomial probability is given below:
- Choose Calc>Probability Distributions>Binomial Distribution.
- Choose Cumulative Probability.
- Enter Number of trials as 200 and Event probability as 0.05.
- In Input constants, enter 14.
- Click OK.
Output obtained from MINITAB is given below:
Probability Density Function
Binomial with ${\displaystyle n=200\text{and}p=0.05}$
$\begin{array}{|cc|}\hline x& P(X=x)\\ 14& 0.0517578\\ \hline\end{array}$
Thus, the probability of getting exactly 14 variegated plants is 0.052.