Explanation:

The normal distribution is also known as the Gaussian distribution or bell curve. It is a continuous probability distribution that is symmetric and unimodal. The distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ).

Shape of Normal Distribution:

The shape of the normal distribution is determined by these two parameters, and it remains the same regardless of their values. The curve is always bell-shaped, with the highest point at the mean and the tails extending infinitely in both directions. The curve is also symmetric, which means that the area under the curve to the left of the mean is equal to the area under the curve to the right of the mean.

Binomial and Poisson Distribution:

The binomial and Poisson distributions are both discrete probability distributions. The binomial distribution describes the number of successes in a fixed number of independent trials, while the Poisson distribution describes the number of events that occur in a fixed interval of time or space.

Both of these distributions have different shapes depending on their parameters. The shape of the binomial distribution is determined by the number of trials and the probability of success, while the shape of the Poisson distribution is determined by the rate parameter.

Conclusion:

In conclusion, the normal distribution is the only distribution that has the same shape regardless of its parameters. This property makes it useful for modeling many real-world phenomena, such as heights, weights, and scores on standardized tests.