Question

SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample

Answer 1

The appropriate solution is "259".

Explanation:

According to the question,

`\sigma = 300`

`M.E=25`

At 82% CI,

`\alpha = 0.18`

Critical value,

`Z_c=1.341`

Now,

The sample size will be:

⇒
`n=(Z_c* (\sigma)/(E) )^2`

By substituting the values, we get

`=(1.341* (300)/(25) )^2`

`=(1.341* 12)^2`

`=259`