Recent questions tagged normal-distribution

Suppose a random variable $Z$ follows $\operatorname{Normal}\left(\mu=0, \sigma^{2}=1\right)$ distribution with probability density function $g(z)$ and cumulative distrib...

Let $X$ and $Y$ be two independent random variables. $X$ follows $\operatorname{Bernoulli}(p=0.3)$ distribution and $Y$ follows $\operatorname{Normal}\left(\mu=0, \sigma^...

Let $X_{1}, X_{2}, \ldots, X_{n}$ be $n$ independent random variables. Each of the random variables follows $\operatorname{Normal}\left(\mu=0, \sigma^{2}=1\right)$ distri...

In June $2017$, a cyberattack named NotPetya spread all over the world. Big companies like Marex, Merck, and FedEx's TNT Express lost a lot of money because of this attac...

Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}...

Consider the statements below related to probability distributions:\textbf{(S1):} For a Poisson distribution, the mean and variance are equal.\textbf{(S2):} For a standar...

The weight of a light bulb has an average of 12.5 grs. with a standard deviation of 2. Assume the variable is normally distributed. If an inspector select randomly a sa...

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{...

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...

Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.

What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?

Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ $0$. How is $Y$ distributed?

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...

1)Among 10000 random digits find probability P that digit 3 appears at most 950 times.(area under normal between Z=0 and Z=1.67 is 0..4525)2)A die is tossed 180 times .us...