Based on history IELTS score is 550 in avg and 30 in standar

Based on history, IELTS score is 550 in avg and 30 in standart deviation. Assume that population follows normal dist.

a) if 9 students in todays toefl exam have been slected at random, final score of them are: 550,520,530,540,550,550,560,570,600. find the sample mean and sample variance.

b) if 16 students are randomly selected, find P(|Xbar - 550| < 15)

What I\'m having problem is part b. Can someone explain me which formula we use and what happens?

Solution

Average of IELTS Score = 550

std dev = 30

Population follows normal

a) n = 9

Sample mean = Total of 9 samples/9 = 552.22

Std dev = 21,999

b_ n =16 Hence std error = pop std dev/rt n = 30/4 =7.5

Hence P(x bar - 550| < 15) = P|Xbar - 550|/sigma) < 2) as std error = 7.5

i.e. it is enough if we find std normal variate less than 2

Hence prob = 0.9772