A normal distribution has a mean of 4.1 and a standard deviation of 2.3. The probability that a value from this distribution will be negative equals ________.
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A. B. C. D.B
The z-value of a selected observation, X, from a normal distribution with mean M and standard deviation S equals z = (X-M)/S. in the present case, the z-value of
X = 0 equals -4.1/2.3 = -1.78. Then, the probability that a number Y is negative is the same as the probability of a z-value less than -1.78. Using the Normal probability tables to get P(z < -1.78) is tricky because the table given in the assigned text is only for positive values. To calculate the probability, use the fact that the standard normal distribution is symmetrical about zero. Hence,
P(z < -1.78) = P(z > + 1.78) = 1.0 - 0.9625 = 0.0375.