Suppose that scores on the mathematics part of a test for eighth-grade students follow a Normal distribution with standard deviation σ = 150. You want to estimate the mean score within ±20 with 90% confidence. How large an SRS of scores must you choose? (Round your answer up to the next whole number.)

We need an SRS of scores of at least 153.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

How large an SRS of scores must you choose?

This is at least n, in which n is found when . So

Rounding to the next whole number, 153

We need an SRS of scores of at least 153.