The delay of a circuit path varies from chip to chip following a normal distribution with a mean of 940 ps and a standard deviation of 30 ps. Taking the fraction of a normal distribution within the mean ±2σ to be about 95.4%, which of the following is closest to the fraction of chips whose delay exceeds the clock period of 1,000 ps?

Answer: A. About 2.3%

Standardizing gives z = (1,000 − 940) ÷ 30 = 2, so the fraction of chips beyond the mean +2σ is needed. The fraction outside ±2σ is 100 − 95.4 = 4.6%, and since the normal distribution is symmetric, the upper side alone is 4.6 ÷ 2 = 2.3%. Treating the delay variation as a probability distribution in this way makes it possible to estimate the fraction of chips that fail timing.

• A. Correct. It is the upper tail beyond z = 2, so (100 − 95.4) ÷ 2 = 2.3%.
• B. 4.6% is the fraction outside the mean ±2σ on both sides combined. Only the upper side, where the delay exceeds the period, is asked for.
• C. 95.4% is the fraction within the mean ±2σ.