It is known that 15 percent of all college freshmen at Ivey University leave after their first year.Calculate the interval that contains 99.73 percent of the students who remain if we are looking at a random sample of 300 Ivey University freshmen.
A) $\left[ \begin{array} { l l }
236.45 & 273.55
\end{array} ]\right.$
B) $\left[ \begin{array} { l l }
26.45 & 63.55
\end{array} \right]$
C) $\left[ \begin{array} { l l }
110.25 & 369.75
\end{array} \right]$
D) $\left[ \begin{array} { l l }
38.82 & 51.18
\end{array} \right]$

Question

It is known that 15 percent of all college freshmen at Ivey University leave after their first year.Calculate the interval that contains 99.73 percent of the students who remain if we are looking at a random sample of 300 Ivey University freshmen.
A) $\left[ \begin{array} { l l } 
236.45 & 273.55
\end{array} ]\right.$
B) $\left[ \begin{array} { l l } 
26.45 & 63.55
\end{array} \right]$
C) $\left[ \begin{array} { l l } 
110.25 & 369.75
\end{array} \right]$
D) $\left[ \begin{array} { l l } 
38.82 & 51.18
\end{array} \right]$

Quizplus · Accepted Answer

The mean number of students who remain is $300 \times 0.85 = 255$. The standard deviation is $\sqrt{300 \times 0.15 \times 0.85} \approx 5.64$. Using the 68-95-99.7 rule, the interval is $255 \pm 3 \times 5.64$, which is approximately $[236.45, 273.55]$.

It Is Known That 15 Percent of All College Freshmen [236.45273.55]\left[ \begin{array} { l l } 236.45 & 273.55\end{array} ]\right.[236.45​273.55​]

It Is Known That 15 Percent of All College Freshmen $\left[ \begin{array} { l l } 236.45 & 273.55\end{array} ]\right.$