Question 625817
population mean is equal to 500
population standard deviation is equal to 100
sample of 400 students has a sample mean of 511.
sample mean standard deviation = population standard deviation / square root of sample size.
this becomes;
sample mean standard deviation = 100 / sqrt(400) which is equal to 5.
99% confidence level is achieved within +/- 2.576 standard deviations.
2.576 standard deviations * 5 is equal to +/- 12.88
this means that, at 99% percent confidence level, the sample mean of 511 infers a population mean between 498.12 and 523.88
this also means that, if you took many samples of 400 students each, 99% of the time your sample mean would be between 498.12 and 523.88.
that's my understanding of what they are looking for here.