need help with this thanks Question 1Suppose X is a random variable with mean 10 and variance 9. Then P( 4

Answered: Suppose X is a random variable with…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 22E

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Step 1

Question 1:

Let X is a random variable with mean 10 and variance 9.

The value of $P (4 < X < 16)$ is,

$\begin{array}{rcl} P (4 < X < 16) & = & P (\frac{4 - 10}{3} < \frac{X - μ}{σ} < \frac{16 - 10}{3}) \\ = & P (- 2 < z < 2) \\ = & P (z < 2) - P (z < - 2) \end{array}$

The probability of z less than –2 can be obtained using the excel formula “=NORM.S.DIST(–2,TRUE)”. The probability value is 0.02275.

The probability of z less than 2 can be obtained using the excel formula “=NORM.S.DIST(2,TRUE)”. The probability value is 0.97725.

The required probability is,

$\begin{array}{rcl} P (4 < X < 16) & = & P (z < 2) - P (z < - 2) \\ = & 0.97725 - 0.02275 \\ = & 0.9545 \\ > & 0.5 \end{array}$

The value of $P (4 < X < 16)$ is 0.9545.

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