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).[
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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