The average score on a standardized test is 750 points with a standard deviation of 50 points. What is
the probability that a student scores more than 700 on the standardized test?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
34%
To find the probability that a student scores more than 700 on the standardized test, we can use the standard normal distribution and convert the scores to z-scores.
First, let's calculate the z-score for 700 using the formula: z = (x - μ) / σ
Where:
x = the score (700)
μ = the mean (750)
σ = the standard deviation (50)
z = (700 - 750) / 50
z = -50 / 50
z = -1
Now that we have the z-score, we can use a z-table or a calculator to find the corresponding probability.
Since we want to find the probability that a student scores more than 700, we need to find the area to the right of the z-score of -1. This area represents the probability that a student scores above 700.
Using a standard normal distribution table or a calculator, we can find that the area to the right of -1 is approximately 0.8413.
Therefore, the probability that a student scores more than 700 on the standardized test is approximately 0.8413 or 84.13%.