Question

The figure shows the probability distribution of a discrete random variable $\mathrm{X}$. Which of the following best describes this random variable?

a. Binomial with $n=8,p=0.1$

b. Binomial with $n=8,p=0.3$

c. Binomial with $n=8,p=0.8$

d. Geometric with $p=0.1$

e. Geometric with $p=0.2$

Short answer

$X$is a random variable with a binomial distribution of $8$and a probability of$0.3$.

Step-by-step solution

Given information

According to the graph, the probability distribution is as follows:

$X$	0	1	2	3	4	5	6	7	8
$P\left(X\right)$	$0.05$	$0.20$	$0.30$	$0.25$	$0.15$	$0.05$	0.01	$0.00$	$0.00$

Explanation for correct option

The probability distribution given can be written as follows:

$$\begin{gathered} P(x=0)=0.05,P(x=1)=0.20 \\ P(x=2)=0.25,P(x=3)=0.25 \\ P(x=4)=0.15,P(x=5)=0.25 \\ P(x=6)=0.01,P(x=7)=0.00122 \\ P(x=8)=0.00007 \end{gathered}$$

Therefore, the total number of trails is 8, with a success probability of$0.3$.

Hence, the random variable X has a binomial distribution with a mean of 8 and a probability of $0.3$.

As a result, "b" is the correct answer.

Explanation for incorrect option

Option A does not describes this random variable of Binomial with $n=8,p=0.1$

Option C does not describes this random variable of Binomial with $n=8,p=0.8$

Option D does not describes this random variable of Geometric with $p=0.1$

Option E does not describes this random variable of Geometric with $p=0.2$