d. There are 200 students in a sample. How many of these students will have scores that fall under the score of 41? Mean=45 standard deviation=4
Use the Empirical Rule.
http://www.oswego.edu/~srp/stats/6895997.htm
To find out the number of students who will have scores that fall under the score of 41, we need to calculate the z-score for a score of 41 and use that information to determine the proportion of students who have scores below 41.
The formula to calculate the z-score is:
z = (X - μ) / σ
Where:
- X is the score we want to find the proportion for (in this case, 41)
- μ is the mean score of the sample (45)
- σ is the standard deviation of the sample (4)
Substituting the values into the formula, we have:
z = (41 - 45) / 4
z = -4 / 4
z = -1
Now, we need to find the proportion of students who have scores below a z-score of -1. We can refer to the z-score table or use a statistical calculator.
Looking up the z-score of -1 in the z-score table, we find that the corresponding proportion is approximately 0.1587.
This means that approximately 15.87% of students will have scores below 41.
To find the actual number of students, we can multiply the proportion by the total number of students in the sample (200):
Number of students = Proportion * Total number of students
Number of students = 0.1587 * 200
Number of students ≈ 31.74
Therefore, approximately 31.74 students out of the 200 in the sample will have scores that fall under the score of 41.