To find which of the given values could be a possible value for [tex]\( p \)[/tex] in the range [tex]\( 0.6 < p < 0.6667 \)[/tex], we need to compare each value to this range. Let's go through them one by one:
1. [tex]\(\frac{16}{27}\)[/tex]:
- Converting this to a decimal, [tex]\(\frac{16}{27} \approx 0.5926\)[/tex].
- This value is less than 0.6, so it is not in the range [tex]\(0.6 < p < 0.6667\)[/tex].
2. [tex]\(0.67\)[/tex]:
- This is a decimal value.
- [tex]\(0.67\)[/tex] is greater than [tex]\(0.6667\)[/tex], so it is not in the range [tex]\(0.6 < p < 0.6667\)[/tex].
3. [tex]\(60\%\)[/tex] (which is the same as [tex]\(\frac{60}{100}\)[/tex] or [tex]\(0.6\)[/tex]):
- This is exactly equal to 0.6.
- Since [tex]\(0.6\)[/tex] is not strictly greater than [tex]\(0.6\)[/tex], it is not in the range [tex]\(0.6 < p < 0.6667\)[/tex].
4. [tex]\((0.8)^2\)[/tex]:
- Calculating this, [tex]\((0.8)^2 = 0.64\)[/tex].
- This value lies within the range [tex]\(0.6 < p < 0.6667\)[/tex]. So, it is a possible value for [tex]\(p\)[/tex].
5. [tex]\(\sqrt{\frac{4}{9}}\)[/tex]:
- Calculating this, [tex]\(\sqrt{\frac{4}{9}} \approx 0.6667\)[/tex].
- This value is exactly the upper bound of the range [tex]\(0.6667\)[/tex], so it is not strictly less than [tex]\(0.6667\)[/tex]. Therefore, it does not fit within [tex]\(0.6 < p < 0.6667\)[/tex].
After evaluating all the given values, the only value that satisfies [tex]\(0.6 < p < 0.6667\)[/tex] is:
[tex]\[
(0.8)^2 = 0.64
\][/tex]
Thus, the value of [tex]\( p \)[/tex] that fits the given range is [tex]\( 0.64 \)[/tex].
