Calculate Probability of Values in a Normal Distribution

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The standard deviation of the distribution equals sqrt(723.6) = 26.9. The z-value of -25 equals (-25 + 10.8)/26.9 = -0.53. The z-value of + 25 equals (25 +

10.8)/26.9 = + 1.33. Therefore, the probability that a number Y lies between -25 and + 25 is the same as the z-score lying between -0.53 and + 1.33. Using the

Normal probability tables, we get P(z < 1.33) = 0.9082. Getting P(z < -0.53) can be tricky when the table given is only for positive values. To calculate the probability, use the fact that the standard normal distribution is symmetrical about zero. Hence, P(z < - 0.53) = P(z > 0.53) = 1.0 - 0.7019 = 0.2981. The probability that a number Y lies between -25 and + 25 is then given by P(-0.53 < z < 1.33) = P(z < 1.33) - P(z < -0.53) = 0.9082 - 0.2981 = 0.61.