Question

Let X1, X2, X3 be three independent normal random variables with expected values ?1, ?2, ?3 and variances ?1^2, ?2^2, ?3^2, respectively. If ?1 = 10, ?2 = 20, ?3 = 30 and ?1^2 = ?2^2 = ?3^2 = 12, find P(54 < X1 + X2 + X3 < 72) (round off to second decimal place).

Name: Let X1, X2, X3 be three independent normal random variables with expected values ?1, ?2, ?3 and variances ?1^2, ?2^2, ?3^2, respectively. If ?1 = 10, ?2 = 20, ?3 = 30 and ?1^2 = ?2^2 = ?3^2 = 12, find P(54 < X1 + X2 + X3 < 72) (round off to second decimal place).
Uploaded: 2023-09-17T11:30:42-08:00
Duration: 2 min 29 s
Channel: Adi S
Description: Let X1, X2, X3 be three independent normal random variables with expected values ?1, ?2, ?3 and variances ?1^2, ?2^2, ?3^2, respectively. If ?1 = 10, ?2 = 20, ?3 = 30 and ?1^2 = ?2^2 = ?3^2 = 12, find P(54 < X1 + X2 + X3 < 72) (round off to second decimal place).

          Let X1, X2, X3 be three independent normal random variables with expected values ?1, ?2, ?3 and variances ?1^2, ?2^2, ?3^2, respectively. If ?1 = 10, ?2 = 20, ?3 = 30 and ?1^2 = ?2^2 = ?3^2 = 12, find P(54 < X1 + X2 + X3 < 72) (round off to second decimal place).

Let X1, X2, X3 be three independent normal random variables with expected values ?1, ?2, ?3 and variances ?1^2, ?2^2, ?3^2, respectively. If ?1 = 10, ?2 = 20, ?3 = 30 and ?1^2 = ?2^2 = ?3^2 = 12, find P(54 < X1 + X2 + X3 < 72) (round off to second decimal place).

Added by Jennifer T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/17/2023

Step 1

Since X1, X2, and X3 are independent, the expected value of their sum is the sum of their expected values, and the variance of their sum is the sum of their variances. Expected value: E(X1 + X2 + X3) = E(X1) + E(X2) + E(X3) = 10 + 20 + 30 = 60 Variance: Var(X1 Show more…

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Let X1, X2, X3 be three independent normal random variables with expected values μ1, μ2, μ3 and variances σ1^2, σ2^2, σ3^2, respectively. If μ1 = 10, μ2 = 20, μ3 = 30 and σ1^2 = σ2^2 = σ3^2 = 12, find P(54 < X1 + X2 + X3 < 72) (round off to second decimal place).