Suppose X is a normal random variable with u = 500 and o = 75. Find the value of: а. Р(Х < 750) %3D b. Р(X > 350) c. P(400 < X< 600)

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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)
Transcribed Image Text: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 = 750-50075=25075=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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