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

Answer:

The appropriate solution is "259".

Step-by-step 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:

⇒ $n=(Z_c\times \frac{\sigma}{E} )^2$

By substituting the values, we get

      $=(1.341\times \frac{300}{25} )^2$

      $=(1.341\times 12)^2$

      $=259$