Calculate the Area Under a Normal Distribution between 50 and 75

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First note that the area between two numbers under a probability distribution is the same as the probability of getting a number between those two numbers. The standard deviation of the distribution equals sqrt(625) = 25. The z-value of 50 equals (50-39)/25 = 0.44. The z-value of 75 equals (75-39)/25 = 1.44. Using the

Normal probability tables, we get P(z < 0.44) = 0.67 and P(z < 1.44) = 0.9251. The area between 50 and 75 is then given by P(0.44 < z < 1.44) = P(z < 1.44) - P(z

< 0.44) = 0.9251 - 0.67 = 0.255.