Which of the Following Probabilities is the Greatest for a Standard Normal Distribution?
A. p(-1.5≤z≤-0.5)
B. p(-0.5≤z≤0.5)
C. p(0.5≤z≤1.5)
D. p(1.5≤z≤2.5)
Answer:- B. p(-0.5≤z≤0.5)
A standard normal distribution has mean 0 and a variance of one. It is about 68% of the area under normal curve lies within one standard deviation from mean value (between negative and positive). Probability decreases with the increase in standard deviation from mean.
Option B mentions the range around the mean of +/- 0.5 standard deviations, which is the least supportive measure for failure mode and effect analysis to differentiate between acceptable design or process variations from failures. This has the largest proportion of area under the curve compared to all other wider intervals taken in options A, C and D.
In particular, 68% of the region lies between -1 to +0 standard deviation away from mean. Within a narrower zone of -0.5 to 0. The other three options, A, C and D have wider intervals more removed from the mean so they will be lower probabilities.
Thus, p(-0.5≤z≤0.5) represents the largest probability for a standard normal distribution compared by all other possibilities The closest interval to the mean captures almost all of the total area under the normal curve .
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