The measurement result of a certain physical quantity follows a normal distribution $N \left( 10 , \sigma ^ { 2 } \right)$. Which of the following conclusions is incorrect? A. The smaller $\sigma$ is, the greater the probability that the physical quantity falls in $( 9.9,10.1 )$ in a single measurement. B. The smaller $\sigma$ is, the probability that the physical quantity is greater than 10 in a single measurement is 0.5. C. The smaller $\sigma$ is, the probability that the physical quantity is less than 9.99 equals the probability that it is greater than 10.01 in a single measurement. D. The smaller $\sigma$ is, the probability that the physical quantity falls in $( 9.9,10.2 )$ equals the probability that it falls in $( 10,10.3 )$ in a single measurement.
D For option A: the smaller $\sigma$ is, the more concentrated the data is around $\mu = 10$, so the probability that the measurement result falls in $(9.9, 10.1)$ increases — correct. For option B: by symmetry of the normal distribution, the probability of being greater than 10 is always 0.5 — correct. For option C: by symmetry, the probability of being greater than 10.01 equals the probability of being less than 9.99 — correct. For option D: the probability that the physical quantity falls in $(9.9, 10.0)$ is not equal to the probability that it falls in $(10.2, 10.3)$, so the two intervals do not have equal probability — incorrect.
The measurement result of a certain physical quantity follows a normal distribution $N \left( 10 , \sigma ^ { 2 } \right)$. Which of the following conclusions is incorrect?
A. The smaller $\sigma$ is, the greater the probability that the physical quantity falls in $( 9.9,10.1 )$ in a single measurement.
B. The smaller $\sigma$ is, the probability that the physical quantity is greater than 10 in a single measurement is 0.5.
C. The smaller $\sigma$ is, the probability that the physical quantity is less than 9.99 equals the probability that it is greater than 10.01 in a single measurement.
D. The smaller $\sigma$ is, the probability that the physical quantity falls in $( 9.9,10.2 )$ equals the probability that it falls in $( 10,10.3 )$ in a single measurement.