Answer:
So, the required sample size is , that she will need to be 95% confident that her sample mean will be within 15 seconds of the true mean.
Step-by-step explanation:
Given that,
Standard deviation () = 40
and we have to find how large a sample is needed to be 95% confident that her sample mean will be within 15 seconds of the true mean.
Now,
If is used as an estimate of , we can be % confident that the error will not exceed a specified amount when the sample size is
........ (i)
where is the z value leaving an area of to the right.
So,
% = 95%
We have and , Now using equation (i), the required sample size is,
........(ii)
Now we have to find the value of .
So, the is the z-value leaving an area of 0.025 to the right {the area left of the is (1-0.025) = 0.975.}
Using Normal Probability table, we see that the closest z-value which leaving an area of 0.025 to the right (i.e. an area of 0.975 to the left) is
Now,
Using equation (ii),
=
≈
So, the required sample size is