The shape of the cumulative distribution function of Gaussian distribution is S-shaped.

The cumulative distribution function (CDF) of a Gaussian distribution, also known as a normal distribution, is a mathematical function that describes the probability of a random variable taking on a value less than or equal to a given value. The CDF is a function of the standard deviation and mean of the distribution.

Properties of the CDF of a Gaussian Distribution:
- The CDF of a Gaussian distribution is a continuous function that ranges from 0 to 1.
- The CDF is symmetric around the mean of the distribution.
- The CDF is S-shaped, meaning it starts from a low value, gradually increases, and then levels off as it approaches 1.

Explanation:
- A straight line at a 45 degrees angle (option 'a') does not describe the shape of the CDF of a Gaussian distribution. The CDF is not a linear function and does not increase at a constant rate.
- A horizontal line (option 'd') also does not describe the shape of the CDF. A horizontal line would indicate that the probability of the random variable being less than or equal to any value is constant, which is not the case for a Gaussian distribution.
- Bell-shaped (option 'b') describes the shape of the probability density function (PDF) of a Gaussian distribution, not the CDF. The PDF represents the relative likelihood of different outcomes, while the CDF represents the cumulative probability up to a certain value.
- The correct answer is option 'c', S-shaped. The CDF of a Gaussian distribution starts from a low value, gradually increases as the value of the random variable increases, and then levels off as it approaches 1. This S-shaped curve is characteristic of the CDF of a Gaussian distribution.

In summary, the shape of the cumulative distribution function of a Gaussian distribution is S-shaped, gradually increasing from a low value to 1 as the value of the random variable increases.

The image below shows a Normal Distribution Curve, and a Cumulative Distribution of that Normal (Gaussian) Distribution.