Question
On a nationwide test taken by high schodi stubents, the thean soore was 52 and whe standard devation was 13 . the sodres were notmally distributad. Complete
the following statements.
(a) Approximately ? 8 of the students scored between 39 and 65
(b) Approximately
the following statements.
(a) Approximately ? 8 of the students scored between 39 and 65
(b) Approximately
Ask by Bowman Chang. in the United States
Mar 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) Approximately 68% of the students scored between 39 and 65.
(b) Approximately 99.7% of the students scored between 13 and 91.
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock Answered by UpStudy AI and reviewed by a Professional Tutor
Like
The Deep Dive
Here’s a bit of fun with your stats! To find out approximately how many students scored between 39 and 65, you can use the empirical rule, which states that about 68% of the scores fall within one standard deviation from the mean. Since 39 (52 - 13) is one standard deviation below the mean and 65 (52 + 13) is one standard deviation above, about 68% of students scored in that range.
For part (b), let’s keep the math rolling! According to the 68-95-99.7 rule, approximately 99.7% of students score within three standard deviations from the mean. So we calculate: 52 - 3(13) = 3 and 52 + 3(13) = 101. Therefore, approximately 99.7% of the students scored between 3 and 101. Look at you, mastering the normal distribution!
