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The value of mortgage loans made by a certain bank one year were normally distributed with...

The value of mortgage loans made by a certain bank one year were normally distributed with a mean of $120,000 and a standard deviation of $40,000. What is the probability that a randomly selected mortgage loan was in the range of $40,000 to $200,000? (Round your answer to 4 decimal places).[

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that ,

mean = = 120000

standard deviation = =40000   

P(40000< x < 200000) = P[(40000 - 120000) /40000 < (x - ) / < (200000 - 120000) / 40000)]

= P( -2< Z < 2)

= P(Z <2 ) - P(Z < -2)

Using z table   

= 0.9772 - 0.0228

probability= 0.9544

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