Continuous Probability Distributions

If $X \sim N(\mu, \sigma^2)$, the maximum ordinate is at $X = \mu$ and is given by:

If the random variable $X$ has normal distribution with probability density function $f(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-1)^2/2}, -\infty < x < \infty$, then the value of $\int_1^\infty f(x) dx$ is:

The annual rainfall at a place is normally distributed with mean 1200 mm and standard deviation 200 mm. What is the probability that in a randomly selected year, the rainfall will be greater than 1400 mm? [Given that the area under the standard normal curve between $Z = 0$ and $Z = 1$ is 0.34]

The mean deviation from the mean m in a normal distribution with variance v^2 is approximately :

If the Z-score of normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation is 3, then the value of X for a normal distribution is :

In a normal distribution 10.03% of the items are under 35kg weight and 89.97% of the items are under 80kg weight. What are the mean and standard deviation of the distribution ?

The point of inflexion of Normal (mu, sigma^2) curve are :

In a normal curve, 99% of the observations are included in the range :

In the standard normal distribution, $P(Z \le 0)$ is equal to:

Let $\bar{X}$ be the mean of a random sample of size $5$ from a normal distribution with $\mu = 0$ and variance $\sigma^2 = 125$. Determine $c$ so that $P\{\bar{X} < c\} = 0.90$:

A random variable $X$ is normally distributed with zero mean and unit variance. The variance of $X^2$ is:

In a Binomial distribution, if '$n$' is the number of trials and '$p$' is the probability of success, then the standard deviation is given by: