Sandra scored 60 on a test. The test scores were normally distributed, with a mean of 50 and a standard deviation of 10? What would Sandra's score be?
Sandra scored 60 on a test. The test scores were normally distributed, with a mean of 50 and a standard deviation of 10? Which of the following percentile ranges would contain Sandra's score?
(a) 35-49
(b) 50-64
(c) 65-79
(d) 80-95
80-95
To find Sandra's score, we need to determine the z-score first. The z-score tells us how many standard deviations Sandra's score is away from the mean. It is calculated using the formula:
z = (x - μ) / σ
Where:
- x is the raw score (Sandra's score)
- μ is the mean
- σ is the standard deviation
Plugging in the values from the question, we have:
z = (60 - 50) / 10
z = 1
Now, we can use the z-score to find Sandra's score using the z-score to raw score conversion table or a calculator. However, since the scores are normally distributed, we can take the z-score and multiply it by the standard deviation and then add it to the mean:
Score = (z * σ) + μ
Plugging in the values:
Score = (1 * 10) + 50
Score = 10 + 50
Score = 60
Therefore, Sandra's score would be 60.