(Solved): Some students are trying to calculate P (p< 0.75) . Other information in the problem indicat ...

Some students are trying to calculate P (p< 0.75) . Other information in the problem indicated that p = 0.6 and n = 64 . Explain what mistake each student made, then calculate the actual correct answer.

2.) [5 points] Some students are trying to calculate \( P(\hat{p}<0.75) \). Other information in the problem indicated that \( p=0.6 \) and \( n=64 \). Explain what mistake each student made, then calculate the actual correct answer. a.) Hyr Young said that since \( \hat{p} \) can only be between 0 and 1 , and \( 0.75 \) is in between, the probability should be \( 0.75 \). b.) Ebony said that we need to look \( 0.75 \) up on the normal table, and after doing that, she found the probability to be \( 0.7734 \). c.) Malik said that he needed to convert to z-values first, and he did this by calculating \( z=\frac{.75-.6}{\left(\sqrt{\frac{(.75)(.25)}{64}}\right)}=\frac{.15}{(0.0541)}=2.77 \). He then found his probability on the normal table and got \( 0.9972 \). d.) Will agreed that he should first convert to a z-value, and he did this by calculating \( z=\frac{.75-.6}{\left(\sqrt{\frac{(.6)(.4)}{64}} /\right.}=\frac{.15}{\left(\frac{.0612}{8}\right)}=\frac{.15}{.00765}=19.60 \). He then found said this was so far off the table, the probability must be close to 1 . The actual correct answer should be the following: