SOLUTION: The monthly utility bills are normally distributed with a mean value of $160 and a standard deviation of $25. (a) Find the probability of having a utility bill between 120 and 180

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Question 600420: The monthly utility bills are normally distributed with a mean value of $160 and a standard deviation of $25.
(a) Find the probability of having a utility bill between 120 and 180.
(b) Find the probability of having a utility bill less than $120.
(c) Find the probability of having a utility bill more than $210.
Answer by sniper619(1) (Show Source):
You can put this solution on YOUR website!
a) P(120< x <180) = P( (120-160/25)< z < (180-160/25) )
= P( -1.6 < z < 0.8)
= P(z < 0.8) - P(z > 1.6)
= 0.7881 - (1-0.9452)
= 0.7881 - 0.0548
= 0.7333
b) P( x<120 ) = P( z < (120-160/25) )
= P( z < -1.6 )
= 1 - 0.9452
= 0.0548
c) P( x>210 ) = P( z > (210-160/25) )
= P( z > 2 )
= 1 - 0.9772
= 0.0228
Note: Used a Normal Distribution Function Table.