Solution Found!
Scores on a standardized test are approximately normally
Chapter 4, Problem 7E(choose chapter or problem)
Scores on a standardized test are approximately normally distributed with a mean of 480 and a standard deviation of 90.
a. What proportion of the scores are above 700?
b. What is the 25th percentile of the scores?
c. If someone’s score is 600, what percentile is she on?
d. What proportion of the scores are between 420 and 520?
Questions & Answers
QUESTION:
Scores on a standardized test are approximately normally distributed with a mean of 480 and a standard deviation of 90.
a. What proportion of the scores are above 700?
b. What is the 25th percentile of the scores?
c. If someone’s score is 600, what percentile is she on?
d. What proportion of the scores are between 420 and 520?
ANSWER:Step 1 of 7
Let \(X\) denote the score on a standardized test.
Then it is approximately normally distributed with mean \(\mu_{\text {is } ~} 480\) and standard deviation \(\sigma\) is 90. Our goal is:
a). We need to find the proportion of the scores above 700 .
b). We need to find the probability of the 25 th percentile of the scores.
c). If someone's score is 600 and we need to find the percentile she is on.
d). We need to find that the proportion of the scores are between 420 and 520.