Answer to Question #189377 in Statistics and Probability for Yusha

Question

Ministry of Education put a guideline that maximum of 30% students 

are allowed to be in campus to control the spread of Covid-19. In average, 13 students 

will come to Statistics class with standard deviation of 3 students. A sample of 20 

students are chosen. Find probability that the average number of students come to 

Statistics class is at least 18?

Answer 1

$\mu = 13 \\ \sigma = 3 \\ n = 20 \\ P(\bar{x}>18) = 1 -P(Z<\frac{\bar{x}- \mu}{\sigma / \sqrt{n}}) \\ =1 -P(Z<\frac{18-13}{0.6711}) \\ = 1 -P(Z<7.45) \\ = 1 -0.9999 \\ = 0.001$