You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 58.2 σ=58.2. You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

represent the sample mean

population mean (variable of interest)

represent the population standard deviation

n represent the sample size  

represent the margin of error desire

The margin of error is given by this formula:

   (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be and the critical value , replacing into formula (b) we got:

So the answer for this case would be n=22547 rounded up to the nearest integer

a

step-by-step explanation: