Question

a university has 40,440 students. in a random sample of 165 students, 11 speak three or more languages. predict the number of students at the university who speak three or more languages. the expected number of students at the university who speak three or more languages is \boxed{}

Explanation:

Step1: Find the proportion in the sample

The proportion of students who speak three or more languages in the sample is the number of such students divided by the sample size. So, the proportion \( p=\frac{11}{165} \).

Step2: Multiply the proportion by the total number of students

To find the expected number of students in the entire university, we multiply this proportion by the total number of students (40440). So the calculation is \( 40440\times\frac{11}{165} \). First, simplify \( \frac{40440}{165} \): \( 40440\div165 = 245.0909\cdots\) (but actually, \( 165\times245 = 40425 \), \( 40440 - 40425 = 15 \), so \( \frac{40440}{165}=\frac{40425 + 15}{165}=245+\frac{15}{165}=245+\frac{1}{11}\approx245.09 \), but better to do \( 40440\div165 = 245.0909\cdots\), then multiply by 11: \( 245.0909\cdots\times11 = 2696 \) (exact calculation: \( 40440\div165 = 245.0909\cdots\), \( 245.0909\cdots\times11 = (245 + \frac{1}{11})\times11 = 245\times11+1 = 2695 + 1 = 2696 \)).

Answer:

2696