The mean scale score on the mathematics examinatin of ninth graders in Texas was 86 with a standard deviation of 5 points. Given a student was selected at random what is the probability that his score was 91 or higher
To find the probability that a student's score is 91 or higher, we need to calculate the z-score and then use a standard normal distribution table.
The z-score measures how many standard deviations a score is from the mean. It can be calculated using the formula:
z = (x - μ) / σ
Where:
- x is the score we are interested in (91 in this case)
- μ is the population mean (86 in this case)
- σ is the standard deviation (5 in this case)
Plugging in the values, we get:
z = (91 - 86) / 5
z = 5 / 5
z = 1
Now that we have the z-score, we can use a standard normal distribution table to find the probability. The probability can be interpreted as the area under the standard normal distribution curve to the right of the z-score of 1.
Using the standard normal distribution table, we can find that the probability of getting a z-score of 1 or higher is approximately 0.8413. This means that there is a 84.13% probability that a randomly selected student from the population will have a score of 91 or higher on the mathematics exam.
So, the probability that the student's score was 91 or higher is approximately 0.8413 or 84.13%.