Answer:
To find the probability that a randomly selected elementary student scores under 600 on the national test, we can use the z-score formula and the standard normal distribution table.
The z-score formula is:
\[ z = \frac{x - \mu}{\sigma} \]
Where:
- \( x \) is the score we want to find the probability for (600 in this case),
- \( \mu \) is the mean of the distribution (500 in this case), and
- \( \sigma \) is the standard deviation of the distribution (90 in this case).
Substituting the values into the formula:
\[ z = \frac{600 - 500}{90} = \frac{100}{90} \approx 1.1111 \]
Next, we look up the z-score of 1.1111 in the standard normal distribution table. The table gives us the probability of obtaining a z-score less than or equal to 1.1111.
From the standard normal distribution table, we find that the probability corresponding to a z-score of 1.1111 is approximately 0.8665.
So, the probability that a randomly selected elementary student scores under 600 on the national test is approximately 0.8665 or 86.65%.
