Final Answer:
The z score to 2 places after the decimal point is 2.73
This score is considered: Not Unusual.
Step-by-step explanation:
The z-score is a measure that describes the position of a single score in relation to the mean of the dataset. It is calculated by subtracting the mean from the score in question and then dividing by the standard deviation.
Here's the formula to calculate z-score:
z = {(X - μ)}/{σ}
Where:
z is the z-score.
X is the score in question.
μ is the mean of the scores.
σ is the standard deviation of the scores.
Given:
The mean score μ is 76.
The standard deviation σ is 2.2.
The individual student's score (X) is 82.
Now, we will apply these values to the z-score formula:
z = {(82 - 76)}/{2.2}
z = {6}/{2.2}
z ≈ 2.73
Rounding the z-score to two decimal places, it becomes approximately 2.73.
A z-score tells us how many standard deviations an element is from the mean.
In statistics, a z-score above 3 or below -3 is typically considered unusual, because this would mean the score is more than 3 standard deviations away from the mean, which happens very rarely in a normal distribution (this would represent well under 1% of the data, assuming a normal distribution).
Since the z-score we obtained is 2.73, which is lower than 3 and higher than -3, this score would not be considered unusual. Hence, we say:
Z-Score: 2.73
This score is considered: Not Unusual
Complete question:
On a recent quiz, the class mean was 76 with a standard deviation of 2.2. Calculate the z score for a person who received score of 82. Z Score: Round the z score to 2 places after the decimal point, if necessary. Is this score considered unusual? Unusual Not Unusual