Normal Distribution properties

Q.

The area (in percentage) under standard normal distribution curve of random variable Z within limits from -3 to +3 is _____.

1. 99.7

Q. If f(x) is a continous real valued random variable defined over the interval $(-\infty ,+\infty )$ and its occurance is defined by the density function given as $f\left(x\right)=\frac{1}{\sqrt{2\pi }b}exp\{-\frac{1}{2}{\left(\frac{x-a}{b}\right)}^2\}$ where a and b are the statistical attributes of the random variable {x}. The value of the integral ${\int }_{-\infty }^a\frac{1}{\sqrt{2\pi }b}exp\{-\frac{1}{2}{\left(\frac{x-a}{b}\right)}^2\}dx\text{is}$

1. 1
2. 0.5
3. $\pi$
4. $\pi /2$

Q. Number of tigers in a reserve is normally distributed with mean and variance respectively as $1200and9\times {10}^4$. The probability of finding more than 1800 tigers is approximately.

1. 0.0125
2. 0.025
3. 0.05
4. None of these

Q.

Let $X_1,X_2\text{and}{X}_3$ be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability $P(X_1+X_2\le X_3)$ is the largest} is .

1. 0.16

Q. The value of $\frac{1}{\sqrt{2\pi }}{\int }_0^{\infty }exp\left(\frac{-x^2}{8}\right)dx$ is.

1. 1

Q. Let U and V be two independent zero mean Gaussian random variables of variances $\frac{1}{4}\text{and}\frac{1}{9}$ respectively. The probability $P(3V\ge 2U)\text{is}$

1. $\frac{4}{9}$
2. $\frac{1}{2}$
3. $\frac{2}{3}$
4. $\frac{5}{9}$

Q. Let X be a normal random variable with mean 1 and variance 4. The probability P(X < 0) is

1. 0.5
2. greater than zero and less than 0.5
3. greater than 0.5 and less than 1.0
4. 1.0

Q. A normal random variable X has the following probability density function

$f_x\left(x\right)=\frac{1}{\sqrt{8\pi }}{e}^{-\left\{\frac{(x-1{)}^2}{8}\right\}},-\infty <x<\infty$

Then ${\int }_1^{\infty }{f}_x\left(x\right)dx?$

1. 0
2. $\frac{1}{2}$
3. $1-\frac{1}{e}$
4. 1

Q. A simple random sample of 100 observations was taken from a large population. The sample mean & the standard deviation were determined to be 80 and 12 respectively. The standards error of mean is

1. 1.2

Q. Consider a Gaussian distributed random variable with zero mean and standard deviation $\sigma .$ The value of its cumulative distribution function at the origin will be

1. 0
2. 0.5
3. 1
4. $10\sigma$