CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is normally distributed with mean 120 and standard deviation 15, which value of X corresponds to the standard normal variate Z = -1.2?
The value is 102. Since X equals the mean plus Z times the standard deviation, X = 120 + (-1.2 x 15) = 120 - 18 = 102. A negative Z means the value lies below the mean, by 1.2 standard deviations.
- A102Correct
- B138
- C105
- D135
Explanation
Z = (X - mean)/SD, so X = 120 + (-1.2)(15) = 120 - 18 = 102. Option 138 results from ignoring the negative sign (120 + 18). The others use wrong multiples of the SD.
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