retagged by
621 views

2 Answers

0 votes
0 votes
There is a 68–95–99.7 rule for a normal random variable.

Beyond one standard deviation, we have 31.8% of the points.
0 votes
0 votes

For standard Random normal distribution variable, the graph looks like this

normal curve

Normal random variable differs from its mean μ by more than σ = (same as saying) = Area under the graph (-infinity to σ) + (σ to infinity)= 100-68.26 = 31.74 i.e. probability of 0.3174  

Related questions

0 votes
0 votes
2 answers
1
Pooja Khatri asked Sep 26, 2018
1,182 views
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
4 votes
4 votes
2 answers
2
Pooja Khatri asked Sep 26, 2018
731 views
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ $0$. How is $Y$ distributed?
0 votes
0 votes
1 answer
3
Pooja Khatri asked Sep 26, 2018
280 views
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
0 votes
0 votes
1 answer
4
Pooja Khatri asked Sep 26, 2018
228 views
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?