On a standardized test, the distribution of scores is normal, the mean of the scores is 75, and the standard deviation is 5.8. If a student scored 83, the student's score ranks
1. below the 75th percentile
2. above the 97th percentile
3. between the 75th percentile and the 84th percentile
4. between the 84th percentile and the 97th percentile
I'm really confused about this problem but im pretty sure i would have to use the standard deviation chart.
Z = (score - mean)/SD
Z score is your score in terms of standard deviations.
You can use your chart, or you can find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score you found.
what is this Of 20 test scores, seven are less than or equal to 80. What is the percentile rank of a test score of 80?
To determine the student's score rank, you can use the standard deviation chart or Z-score formula. Let's use the Z-score formula in this case.
The Z-score measures how many standard deviations a given data point is away from the mean. The formula is:
Z = (X - μ) / σ
Where:
- Z is the Z-score
- X is the data point (score)
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
In this case, X = 83, μ = 75, and σ = 5.8.
Calculating the Z-score:
Z = (83 - 75) / 5.8
Z ≈ 1.38
Now, you can use a Z-score table (standard normal distribution table) to determine the percentile associated with the Z-score.
Looking up the Z-score of 1.38 in the table, you will find that it corresponds to a percentile of approximately 91.71%.
Therefore, the student's score ranks between the 75th percentile and the 84th percentile (option 3).
To determine where the student's score ranks, we need to calculate the percentile of the score.
To do this, we need to convert the student's score to a z-score using the formula: z = (x - μ) / σ
Given:
Mean (μ) = 75
Standard Deviation (σ) = 5.8
Student's Score (x) = 83
Substituting the values,
z = (83 - 75) / 5.8
z = 8 / 5.8
z ≈ 1.3793
Now, we can use a standard normal distribution table or a calculator to find the percentile associated with the z-score.
Looking up the z-score of 1.3793 in the standard normal distribution table, we find that it corresponds to approximately 91.89th percentile.
Since the student's score ranks at the 91.89th percentile, we can conclude that the student's score falls:
1. below the 75th percentile (False)
2. above the 97th percentile (False)
3. between the 75th percentile and the 84th percentile (False)
4. between the 84th percentile and the 97th percentile (True)
Therefore, the correct answer is option 4. The student's score falls between the 84th percentile and the 97th percentile.