Question

For each of the following probability histograms of binomial distributions, specify whether the success probability is less than, equal to, or greater than 0.5. Explain your answers.

Short answer

Histogram (a) $p>0.5$.

Histogram (b)$p=0.5$.

Step-by-step solution

Step 1. Given information.

The given statement is:

For each of the following probability histograms of binomial distributions, specify whether the success probability is less than, equal to, or greater than 0.5.

The given histograms of binomial distributions are shown below:

Step 2. Specify whether the success probability is less than, equal to, or greater than 0.5 for the histogram (a) of a binomial distribution.

A binomial distribution is to be said right skewed if its probability is less than 0.5, it will be symmetric if its probability is 0.5.

Further, it will be left-skewed if its probability is more than 0.5.

Considering the histogram (a) of the binomial distribution, we can observe that the data is left-skewed, implying that the likelihood of success is more than 0.5.

Therefore, for histogram (a)$p>0.5$.

Step 3. Specify whether the success probability is less than, equal to, or greater than 0.5 for the histogram (b) of a binomial distribution.

According to the histogram in part (b), the data is symmetric, which means that the likelihood of success is equal to 0.5.

Therefore, for histogram (b)$p=0.5$.