SOLUTION: If the mean score on a math quiz is 12.8 and 77.0% of the students in your class scored between 9.2 and 16.4 determine the standard deviation of the quiz scores.

Question 1140214:
If the mean score on a math quiz is 12.8 and 77.0%
of the students in your class scored between 9.2 and 16.4
determine the standard deviation of the quiz scores.

The standard deviation of the quiz scores is
.
(Round to one decimal place as needed.)

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
assuming the distribution of the scores are normal, then you get the following.

z = (x - m) / s

z is the z-score
x is the raw score
m is the mean
s is the standard deviation

if the mean is 12.8 and the high score is 16.4, then the formula becomes:

z = 16.4 - 12.8 / s which becomes z = 3.6 / s

if you solve for s, you will get s = 3.6 / z

you need to find z.

you are given that 77% of the scores are between 9.2 and 16.4.

the 77% is assumed to be in the middle of the normal distribution curve.

this means that the tails on either end are the same.

each tail is therefore (100% - 77%) / 2 = 11.5%.

if you look up the z-score that has 11.5% of the normal distribution curve to the left of it, you will find that the z-score is equal to -1.200358858.

that would be the low z-score.
since the normal distribution is symmetric, then the high z-score will be 1.200358858.

you have 77% of the normal distribution is between z-score of -1.200358858. and 1.200358858.

your high z-score formula becomes z = (16.4 - 12.8) / s which becomes 1.200358858 = 3.6 / s.

solve for s to get s = 3.6/1.200358858 which makes s = 2.999103123

that would be your standard deviation.

your mean is 12.8
your standard deviation is 2.999103123
77% of your scores will be between 9.2 and 16.4

RELATED QUESTIONS
the mean test score of 50 students in a statistics class is 80 with a standard deviation... (answered by Boreal)

The distribution of scores on a recent quiz in Mr. Waldron's statistics class is... (answered by Boreal)

A student scored 483 points on a quiz and the students standard or (z) score was -1. the... (answered by stanbon)

on an english quiz three students scored 5, five scored 4 and two students scored 2. find (answered by sofiyac)

In psychology class, 43 students have a mean score of 87.8 on a test. Then 9 more... (answered by math_tutor2020,ikleyn)

Jenna scored 75, 80, and 92 on her Math quizzes. What is the minimum score she needs on... (answered by erica65404)

Karl Schmidt just scored a 96 on his last biology unit test. The mean score of the 36... (answered by stanbon)

There are fifty students in a class. In a 100 marks exam, 20 students scored less than 30 (answered by ankor@dixie-net.com)

If 200 students write a test and the average score is 77%. With a standard deviation of... (answered by Fombitz)