# Recent questions tagged normal-distribution

1 vote
1
Let $X_1,\dots X_{50}$ be independent random variables following $N(0,1)$ distribution. Let $\Sigma _{i=1}^{50} X^2_i,$ and $E(Y)=a$ and $Var(Y)=b.$ Then, the ordered pair $(a,b)$ is: $(50,100)$ $(50,50)$ $(25,50)$ $(25,100)$
2
If $f(x)=k$ exp, $\{ -(9x^2-12x+13)\}$, is a $p, d, f$ of a normal distribution ($k$, being a constant), the mean and standard deviation of the distribution: $\mu = \frac{2}{3}, \sigma = \frac{1}{3 \sqrt{2}}$ $\mu = 2, \sigma = \frac{1}{\sqrt{2}}$ $\mu = \frac{1}{3}, \sigma = \frac{1}{3 \sqrt{2}}$ $\mu = \frac{2}{3}, \sigma = \frac{1}{ \sqrt{3}}$
1 vote
3
In four tests taken by 450 students, marks are found to be normally distributed with mean and variance as given below Test Id Mean Variance 1 74 121 2 75 100 3 78 196 4 82 169 A has secured 80 in the first test, 81 in the second, 86 in the third and 89 in the fourth. In which test did A actually perform best relative to other students. (A)Fourth Test (B)Third Test (C)Second Test (D)First Test
4
Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2 respectively. Consider Y =X1-X2; µ1=µ2=1, σl=1, σ2=2. Then. (a) Y is normal distributed with mean 0 and variance 1 (b) Y is normally distributed with mean 0 and ... (c) Y has mean 0 and variance 5, but is NOT normally distributed (d) Y has mean 0 and variance 1, but is NOT normally distributed
5
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
6
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
7
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ > $0$. How is $Y$ distributed?
1 vote
8
A nationalized bank has found that the daily balance available in its saving bank accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders who maintain an average daily balance more than Rs. 500 is _______________. Explain the calculation of the probability of Z score. Do GATE provide Z score table?
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Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
11
If the mean of a normal frequency distribution of 1000 items is 25 and its standard deviation is 2.5, then its maximum ordinate is $\frac{1000}{\sqrt{2 \pi} } e^{-25}$ $\frac{1000}{\sqrt{2 \pi} }$ $\frac{1000}{\sqrt{2 \pi} } e^{-2.5}$ $\frac{400}{\sqrt{2 \pi} }$
Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P (X ≤ -1) = P (Y ≥ 2)$ , the standard deviation of $Y$ is $3$ $2$ $\sqrt{2}$ $1$