# GATE ME 2013 | Question: 24

Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$  is

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

recategorized

## Related questions

Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? $I$ $II$ $III$ $IV$
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has answered the question ... the correct answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as Exponential Bernoulli Binomial Normal
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$
Let $X_1, \: X_2$ be two independent normal random variables with means $\mu_1, \: \ \mu_2$ and standard deviations $\sigma_1, \: \sigma_2$, respectively. Consider $Y=X_1-X_2; \: \mu_1 = \mu_2 =1, \: \sigma_1=1, \: \sigma_2=2$. Then, $Y$ is normally distributed ... $Y$ has mean $0$ and variance $5$, but is NOT normally distributed $Y$ has mean $0$ and variance $1$, but is NOT normally distributed