Answer:
The minimum score to be obtained to place in the top 10% and win this award is, 557
Explanation:
Since the score obtained by eighth grade students is a normal random variable with a mean
and
and we are interested in the minimum score required for a student to be in the top 10% of all scores, It is necessary to calculate the 90th percentile for the cumulative probability distribution of the score variable in the reading test.
The variable
is a standard normal variable and therefore,
is the score corresponding to the standardized value z.
We must calculate the value of k such that
, then, using the inverse standard normal distribution you have to
y hence

Conclusion: The minimum score to be obtained to place in the top 10% is 557