It may be or may not be; however a normal distribution is unimodal.
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No, the normal distribution is strictly unimodal.
Your distribution is unimodal and symmetrical.
Please consider the probability density function graphs for the beta distribution, given in the link. For alpha=beta=2, the density is unimodal, which is to say, it has a single maximum. In contrast, for alpha=beta=0.5, the density is bimodal; it has two maxima.
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
No. Normal distribution is a continuous probability.