Statistics Help - January 2019 Problem of the Month - Normal Distribution, Z-score

As a number of college students need help with normal distribution, z-score problems, has come up with this exercise. Solving the following problem can help students gain a better understanding and resolve similar conceptual problems.
CAMBRIDGE, Mass. - Jan. 14, 2019 - PRLog -- The following exemplifies a general normal distribution problem normalized into a Z-score problem with usage of the Z-score table. Over 30% of the problems that Tutorteddy encounters are related to calculating Z-value.


Monthly Utility bills are normally distributed with a mean value of $160 and standard deviation of $25.
a. Find probability of bill between $120 and $180
b.Find probability of bill less than $120
c.Find probability of bill more than $210


Define X as the monthly utility bill and Z as a standard normal random variable.
(a) P(120 < X < 180) = P((120-160)/25 < Z < (180-160)/25) = 0.7333
(b) P(X < 120) = P(Z < (120-160)/25) = 0.0548
(c) P(X > 210) = P(Z > (210-160)/25) = 0.0228

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