List of practice Questions

The probability density function \(f(x)\) of a random variable \(X\) which takes real values is
\[ f(x) = \frac{1}{3\sqrt{2\pi}} \exp\left(-\frac{x^2}{18}\right), \quad x \in (-\infty, +\infty) \]
Which one of the following statements is correct about the random variable \(X\)?

The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed with a mean of 160 and standard deviation of 10.
If the probability of age greater than 50 years is equal to the probability of height greater than \(h\), the value of \(h\) (in cm) is ______ (rounded off to two decimal places).