CA Foundation · Quantitative Aptitude · Theoretical Distributions
The delivery time of an e-commerce parcel in Jaipur is normally distributed with mean 60 hours and standard deviation 12 hours. Given P(0 < Z < 1) = 0.3413, what is the probability that a parcel is delivered between 48 and 72 hours?
The probability is 0.6826. The limits 48 and 72 hours standardise to Z = −1 and Z = +1. Because the normal curve is symmetric, the area between them is twice the table value 0.3413, which equals 0.6826.
- A0.3413
- B0.1587
- C0.8413
- D0.6826Correct
Explanation
Z for 48 = (48 − 60)/12 = −1 and Z for 72 = (72 − 60)/12 = 1. By symmetry, P(−1 < Z < 1) = 2 × 0.3413 = 0.6826. Taking only one side, 0.3413, ignores the other half of the interval.
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