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In a symmetric binomial probability distribution, the probability of successes will be equal to that of the failures. In the case of tossing a coin, the probabilitiesof heads and tails are equal, and this can be an example of a symmetric binomial probability distribution

From the definition, as it can be envisaged,the probability will be the same for both variables, and the calculation is shown below:

$\begin{array}{rcl}\text{Probability}& =& \frac{Total  probability}{2}\\ & =& \frac{1}{2}\\ & =& 0.5\\ & & \end{array}$

From the above calculation, it can be envisaged that the probability is 0.5.

Whenever the skewness remains positive (to the right), it means that the value of p must be more than 0.5. As the maximum probability can be upto 1, the value will stay between 0.5 and 1.

d. On the horizontal axis, the probabilities are plotted, and on the horizontal axis, the values are plotted from 1 to 5.In this case, it is symmetric.So, the mean value, 3,shows the highest probability

On the horizontal axis, the probabilities are plotted, and on the horizontal axis, the values are plotted from 1 to 8. In this case, it is positively skewed.So, the mean value, 4,doesnot show the highest probability, but instead, 3 showsthe highest probability.

On the horizontal axis, the probabilities are plotted, and on the horizontal axis, the values are plotted from 1 to 8.In this case, it is negatively skewed.So, the mean value, 4,doesnot show the highest probability, but instead, 6 showsthe highest probability.

Here, the value of p remains 0.5, and it indicates that the mean value of x shows the highest probability.In this case, the left tail remains exactly equal to the right tail when plotted on the graph.

Here, the value of p remains above 0.5, and it indicates that the mean value of x does not show the highest probability.In this case, the right tail remains greater than the left tail when plotted on the graph.

Here, the value of p remains below 0.5, and it indicates that the mean value of x does not show the highest probability.In this case, the left tail remains greater than the right tail when plotted on the graph.