Probability Sheet using Cards and Dice $\downarrow$ 『
Question 8
What percent of the standard normal distribution $\mathrm{N}(\mu=0, \sigma=1)$ is found in the region $\mathrm{Z}> 0.96$ ?
$16.85 \%$
$83.15 \%$
$96.00 \%$
$27.72 \%$
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Step 1 ：First, we calculate the cumulative distribution function (CDF) at 0.96 for a standard normal distribution \(N(\mu=0, \sigma=1)\). The CDF is the probability that a random variable takes a value less than or equal to a certain value. In this case, we find that the CDF at 0.96 is approximately 0.8314723925331622.

Step 2 ：Next, we want to find the probability that the random variable takes a value greater than 0.96. This is given by \(1 - \text{CDF}\). So, we subtract the CDF from 1 to get approximately 0.16852760746683781.

Step 3 ：Finally, we convert this probability to a percentage by multiplying by 100. This gives us approximately 16.85276074668378%.

Step 4 ：The percentage of the standard normal distribution that is found in the region where Z > 0.96 is therefore approximately 16.85%. This matches one of the options given in the question, so we can conclude that our calculation is correct.

Step 5 ：The final answer is \(\boxed{16.85\%}\).