Confidence Intervals Problem

A multiple choice test question is considered easy if at least 80% of the responses are correct. A sample of 6503 responses to one question indicates that 5463 of those responses were correct. Construct the 99% confidence interval for the true proportion of correct responses. Is it likely that this question is really easy?

The t Distribution table can be found here: elementary-statistics-by-Bluman-8th-Edition (page 786 from the book OR 825 of 943 from the pdf).

ognamdik said:

A multiple choice test question is considered easy if at least 80% of the responses are correct. A sample of 6503 responses to one question indicates that 5463 of those responses were correct. Construct the 99% confidence interval for the true proportion of correct responses. Is it likely that this question is really easy?

The t Distribution table can be found here: elementary-statistics-by-Bluman-8th-Edition (page 786 from the book OR 825 of 943 from the pdf).

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this is my solution:

p.hat = 5463/6503 = 0.84
q.hat = 1-0.84 = 0.16
z.sub(alpha/2) = 2.58
E = z.sub(alpha/2)*sqrt[(p.hat)*(q.hat)/n]
= 2.58*sqrt(0.84*0.16/6503)
E = 0.012
(p.hat)-E < p < (p.hat)+E
0.828 < p < 0.852
82.8% < p < 85.2%
*Using 99% confidence level, we can say that the number of correct responses can fall between 82.8% and 85.2%. Since the minimum percentage of correct responses for a question to be considered easy is only 80%, we can conclude that this question is relatively easy.

is this correct?