Question

On a recent statewide math test, the raw score average was 56 points with a standard deviation of 18. If the scores were normally distributed and 24,000 students took the test, answer the following questions. (d) How many of the 24,000 students receive a scaled score greater than a 90%?

Answer 1

To find the number of students who scored higher than a 90%, we first need to convert the 90% score to a z-score using the formula z = (x - μ) / σ, where x is the score we want to convert, μ is the mean, and σ is the standard deviation.

z = (90 - 56) / 18 = 1.89

Using a standard normal distribution table or calculator, we can find that the percentage of students who scored higher than a z-score of 1.89 is 3.22%.

So, the number of students who scored higher than a 90% would be:

0.0322 x 24,000 = 773.28

Rounding to the nearest whole number, we can say that approximately 773 students received a scaled score greater than a 90%.