There are 200 students in a sample. How many of these students will have scores that fall under the score of 41? Mean is 45, standard dev. is 4.
Z = (score-mean)/SD
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. Multiply that proportion by 200.
To determine the number of students who will have scores falling under 41, we need to calculate the z-score and then use the z-table.
1. Calculate the z-score:
The z-score measures how many standard deviations away a particular value is from the mean. We can calculate the z-score using the formula: z = (x - μ) / σ, where x is the given value (41 in this case), μ is the mean, and σ is the standard deviation.
So, z = (41 - 45) / 4 = -1
2. Look up the z-score in the z-table:
The z-table provides the area under the standard normal curve for a given z-score. We need to find the area to the left of the z-score -1.
If we look up the z-score -1 in the z-table, we find that the area to the left is approximately 0.1587.
3. Calculate the number of students:
The area to the left of the z-score represents the proportion or percentage of students who scored below 41. Multiplying this proportion by the total number of students will give us the approximate number of students who scored below 41.
Number of students = Area to the left * Total number of students
= 0.1587 * 200
≈ 31.74
Therefore, approximately 32 students will have scores falling under 41.