Question

Q.10. Let X be a Gaussian random variable with $m = 5$ and $\sigma^2 = 16$. (a) Find $P[X > 4]$, $P[X \ge 7]$, $P[6.72 < X < 10.16]$, $P[2 < X < 7]$, $P[6 \le X \le 8]$. (b) $P[X < a] = 0.8869$, find a. (c) $P[X > b] = 0.11131$, find b. (d) $P[13 < X \le c] = 0.0123$, find c.

          Q.10.
Let X be a Gaussian random variable with $m = 5$ and $\sigma^2 = 16$.
(a) Find $P[X > 4]$, $P[X \ge 7]$, $P[6.72 < X < 10.16]$, $P[2 < X < 7]$, $P[6 \le X \le 8]$.
(b) $P[X < a] = 0.8869$, find a.
(c) $P[X > b] = 0.11131$, find b.
(d) $P[13 < X \le c] = 0.0123$, find c.

Q.10.
Let X be a Gaussian random variable with m = 5 and σ^2 = 16.
(a) Find P[X > 4], P[X ≥ 7], P[6.72 < X < 10.16], P[2 < X < 7], P[6 ≤ X ≤ 8].
(b) P[X < a] = 0.8869, find a.
(c) P[X > b] = 0.11131, find b.
(d) P[13 < X ≤ c] = 0.0123, find c.

Added by Shane C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ramesh Rajak

10/26/2021

Step 1

Therefore, the standard deviation is $\sigma$ = 4. Show more…

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Q.10. Let X be a Gaussian random variable with m = 5 and $\sigma^2$ = 16. (a) Find P[X > 4], P[X ≥ 7], P[6.72 < X < 10.16], P[2 < X <7], P[6 ≤ X ≤ 8]. (b) P[X < a] = 0.8869, find a. (c) P[X > b] = 0.11131, find b. (d) P[13 < X ≤ c] = 0.0123, find c.