Test score are normally distributed with a mean of 500 and a standard deviation of 50. What percentage of students scored below a 575?
a
93.32%
b
50%
c
56.68%
d
6.68%
https://davidmlane.com/hyperstat/z_table.html
To find the percentage of students who scored below 575, we need to calculate the z-score for that value and then look it up in the standard normal distribution table.
To calculate the z-score, we use the formula:
z = (x - mean) / standard deviation
In this case, the mean is 500 and the standard deviation is 50. Plugging in the values:
z = (575 - 500) / 50
z = 75 / 50
z = 1.5
Now, we can look up the z-score of 1.5 in the standard normal distribution table. The table will give us the area under the curve to the left of the z-score.
According to the standard normal distribution table, the area to the left of z-score 1.5 is 0.9332.
This means that approximately 93.32% of students scored below a 575.
So, the correct answer is option a) 93.32%.