Sample Proportion

In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution.

Four hundred students are randomly selected from the college, and 224 of them will transfer to a college in the CSU system.

Determine the sample proportion p these students who will transfer to a college in the CSU system.

Correct answer:

P =  0.9333

Step-by-step explanation:

$$\begin{gathered} p=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ n=400 \\ {n}_2=224 \\ \mu =n\cdot p=400\cdot \frac{3}{5}=\frac{400\cdot 3}{5}=\frac{1200}{5}=240 \\ {\sigma }_2=n\cdot p\cdot (1-p)=400\cdot \frac{3}{5}\cdot (1-\frac{3}{5})=96 \\ P=\frac{n_2}{\mu }=\frac{224}{240}=\frac{14}{15}=0.9333 \end{gathered}$$

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