If X is a normal random variable with $\mu = 2$ and $\sigma^2 = 4$, find $P(X < -1)$, $P(X > 0)$, and $P(0 < X < 1)$.
Added by Darlene A.
Close
Step 1
Since $\sigma^2 = 4$, we have $\sigma = \sqrt{4} = 2$. Now, we need to standardize the normal random variable $X$ by converting it to a standard normal random variable $Z$ using the formula $Z = \frac{X - \mu}{\sigma}$. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 71 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If x is a Gaussian (u = -1, σ = 3) random variable, what is P[-4 < X ≤ 1]? What is P[X ≥ 7]? Justify the answers.
Adi S.
If $X$ is a normal random variable with parameters $\mu=10$ and $\sigma^{2}=36,$ compute (a) $P\{X>5\}$ (b) $P\{4<X<16\}$ (c) $P\{X<8\}$ (d) $P\{X<20\}$ (e) $P\{X>16\}$.
Abdul K.
If $X$ is a normal random variable with parameters $\mu=10$ and $\sigma^{2}=36,$ compute (a) $P\{X>5\}$ (b) $P\{4<X<16\}$ (c) $P\{X<8\}$ (d) $P\{X<20\}$ (e) $P\{X>16\}$
Ramesh R.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD