Answer: Choice D
[tex]n( \ 1-\widehat{p}\ ) \ge 10[/tex]
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Explanation:
In order to use a normal distribution to approximate the binomial distribution, we need both of the following to be true
[tex]np \ge 10\\n(1-p) \ge 10[/tex]
Some books will use '5' in place of '10' if they aren't worried about being as strict with the conditions.
If we don't know the population proportion p, then we use the next best thing [tex]\widehat{p}[/tex] which is pronounced "p-hat", since the letter p has a hat on top. The [tex]\widehat{p}[/tex] is the sample proportion, and it estimates the population proportion p.
So if we don't know p, but do know [tex]\widehat{p}[/tex], then we need both of these conditions to be true
[tex]n\widehat{p} \ge 10\\n(\ 1-\widehat{p} \ ) \ge 10[/tex]
The second inequality matches with choice D.
