Ariana's raw score of 33 on her philosophy exam converted to a z-score of -1.50. Claire's raw score on the same exam was 48 and it converted to a z-score of +1.00. What was the standard deviation for the distribution?

Question

Quizplus · Accepted Answer

We can use the formula for z-score:

z = (x - mean) / standard deviation

For Ariana: 
-1.50 = (33 - mean) / standard deviation

For Claire: 
1.00 = (48 - mean) / standard deviation

We can solve for the mean using either equation:

mean = x - z * standard deviation

For Ariana: 
mean = 33 - (-1.50) * standard deviation = 33 + 1.50 * standard deviation

For Claire: 
mean = 48 - (1.00) * standard deviation = 48 - 1.00 * standard deviation

Setting these two expressions equal to each other:

33 + 1.50 * standard deviation = 48 - 1.00 * standard deviation

Solving for standard deviation:

2.50 * standard deviation = 15

standard deviation = 6

Therefore, the answer is B) 6.

Ariana's Raw Score of 33 on Her Philosophy Exam Converted