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The probability density of a particle in an energy eigenfunction of a one-dimensional infinite square well is displayed. Restart. The probability density is used to determine the probability that the particle's position will lie in an interval. For the probability density shown in the animation:

1. Verify that the probability that the particle is somewhere, is 1.
2. Find the probability that the particle is located between x = 0.30 and x = 0.32.
3. Find the probability that the particle is located in the left-hand side of the region (0 > x > 0.5).
4. Calculate the expectation value of x---the probability density is given by 2*sin²(pi*x).
5. Calculate the standard deviation of the distribution.

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