On a test with a mean of 50 and a standard deviation of 3, a person gets a z-sco
ID: 3204656 • Letter: O
Question
On a test with a mean of 50 and a standard deviation of 3, a person gets a z-score of 2.5. What is the person’s test score? 6. A person gets a test score of 60 and a z-score of 1.5 on a test with a standard deviation of 6. What is the mean of the test scores? 7. A person gets a test score of 54 and a z-score of –.75 on a test with a mean of 56. What is the standard deviation of the test scores? 8. A person gets a score of 86 on a test with a mean of 75 and standard deviation of 8. What would the person’s score be on a scale with a mean of 200 and standard deviation of 25?
Explanation / Answer
5)
mean = 50, std. deviation = 3 , z score = 2.5
By normal distribution,
z = (X - mean) / std. deviation
2.5 = ( X - 50 )/ 3
X = 57.5
6)
X = 60 , z score = 1.5 , std. deviation = 6
By normal distribution,
z = (X - mean) / std. deviation
1.5 = (60 - mean )/ 6
mean = 51
7)
X = 54 , z score = -.75 , mean = 56
By normal distribution,
z = (X - mean) / std. deviation
-.75 = ( 54 - 56 )/ std. deviation
std. deviation = 2.67