find the value of the probability of the standard normal variable Z corresponding to the shared area under the standard normal curve. 20. Suppose X is a normal random variable with u = 500 ando = 75. Find the value of:а. Р(X < 750)b. Р(X > 350) с. Р(400 < X < 600)

Answered: Suppose X is a normal random variable…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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find the value of the probability of the standard normal variable Z corresponding to the shared area under the standard normal curve.

20. Suppose X is a normal random variable with u = 500 and
o = 75. Find the value of:
а. Р(X < 750)
b. Р(X > 350) с. Р(400 < X < 600)

Expert Solution

Step 1

We are given that
X is a normal random variable with $μ = 500$ and $σ = 75$ .

We have to find the value of

a)P(X<750)

Using the z-transform formula, we get
$z = \frac{750 - 500}{75} = \frac{250}{75} = 3.33$
From the standard normal distribution table, we find the value of P(z<3.33) = 0.99957
So, we get P(X < 750) = 0.99957

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