Question

The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 99% confidence. How large a sample should she take to ensure that the margin of error is below 24? (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your final answer to the nearest whole number.)

Answer 1

it is given that range is 200 to 800

using range rule of thumb, standard deviation =(higher value - lower value)/4

= (800-200)/4

= 600/4

= 150

and margin of error(ME) = 24

z score for 99% confidence interval using z distribution table is z = 2.576

Formula for sample size is

setting the given values, we get

Rounding to nearest whole number , we get sample size n = 259