A standard math test was given to 6000 students. The scores were normally distributed with a mean of 420 and a standard deviation of 40. If george scored 340, how many students scored more than George? This is hrd because I tried using calculator but that's not the help i need. I need to know how to solve it??
hard*
you can play around with Z table stuff here:
http://davidmlane.com/hyperstat/z_table.html
I cant use that table when Im taking a test or exam I would need to know the steps since its a online class?
without a Z table there is no way to do this stuff. Not unless you can calculate the normal distribution stuff by hand.
There may be a chance that they will provide a few Z scores at test time, and if so, then you can interpolate.
Otherwise, check your class materials and there should be some way to figure the stuff by hand.
Are you allowed to use the table in your statistics text labeled something like "areas under normal distribution"?
To solve this question, you need to use the concept of z-scores and the standard normal distribution.
1. Calculate the z-score for George's score:
z = (x - μ) / σ
where:
- x is George's score (340 in this case),
- μ is the mean of the distribution (420 in this case),
- σ is the standard deviation of the distribution (40 in this case).
Substituting the values into the formula:
z = (340 - 420) / 40
z = -2
2. Look up the z-score in the standard normal distribution table (also known as the z-table) to find the corresponding percentile. The percentile represents the proportion of values that fall below a certain z-score.
From the z-table, a z-score of -2 corresponds to a percentile of approximately 0.0228.
3. Since we want to find the number of students who scored more than George (i.e., above his score), we subtract the percentile from 1 to find the proportion of students who scored equal to or above his score:
Proportion = 1 - 0.0228
Proportion ≈ 0.9772
4. Now, we can calculate the number of students who scored more than George by multiplying the proportion by the total number of students (6000 in this case):
Number of students = Proportion * Total number of students
Number of students = 0.9772 * 6000
Number of students ≈ 5863.2
Therefore, approximately 5863 students scored more than George on the test. Keep in mind that we're dealing with whole numbers, so you would round this value to the nearest whole number. In this case, the answer would be 5863 students.