Question

One large course has 900 students, broken down into section meetings with 30 students each. The section meetings are led by teaching assistants. On the final, the class average is 63, and the SD is 20. However, in one section the average is only 55. The TA argues this way: If you took 30 students at random from the class, there is a pretty good chance they would average below 55 on the final. That’s what happened to me—chance variation. Is this a good defense? Answer yes or no, and explain briefly.

Answer 1

Answer

given,

Number of student = 900

average of class(μ) = 63

student in each section (n) = 30

standard deviation of class = 20

average on another section be 55

To find the probability that average is below 55 on the final.

now,

$P(\bar{x}<55)$

$P(\dfrac{\bar{x}-\mu}{\dfrac{s}{\sqrt{n}}}<\dfrac{55-63}{\dfrac{20}{\sqrt{30}}})$

$P(z <\dfrac{55-63}{\dfrac{20}{\sqrt{30}}})$

$P(z <\dfrac{-8}{3.651}})$

$P(z < -2.19)$

= 0.0143 (from normal table)

Since the probability is small, there is not a good chance they would avg below 55 on the final.