The average score on a standardized test is 500 points with a standard deviation of 50 points. If 2,000

students take the test at a local school, how many students do you expect to score between 450 and 550
points?

im looking for the answer!!!

To find the number of students you expect to score between 450 and 550 points, you need to calculate the proportion of students within that range. Here's how:

Step 1: Determine the Z-scores for each boundary. The Z-score represents the number of standard deviations a data point is from the mean.

For the lower boundary score of 450 points:
Z = (450 - 500) / 50

For the upper boundary score of 550 points:
Z = (550 - 500) / 50

Step 2: Use a standard normal distribution table or a calculator to find the area under the normal curve corresponding to each Z-score. This will give you the proportion of students who scored between the two boundaries.

Step 3: Multiply the proportion found in Step 2 by the total number of students taking the test (2,000). This will give you the expected number of students who scored between 450 and 550 points.

Let's calculate it:

For the lower boundary of 450 points:
Z1 = (450 - 500) / 50 = -1.00

Using a standard normal distribution table or a calculator, you can find that the area to the left of Z = -1.00 is approximately 0.1587.

For the upper boundary of 550 points:
Z2 = (550 - 500) / 50 = 1.00

The area to the left of Z = 1.00 is also approximately 0.1587.

Now, we can calculate the proportion between the two boundaries:
Proportion between boundaries = area to the left of Z2 - area to the left of Z1 = 0.1587 - 0.1587 = 0.0000

Finally, multiply this proportion by the total number of students:
Expected number of students = Proportion between boundaries * Total number of students = 0.0000 * 2000 = 0

Therefore, you would expect 0 students to score between 450 and 550 points in this particular scenario.

Z = (score-mean)/SD

Calculate Z and find its proportion in table in the back of your stats book labeled "areas under normal distribution". Convert proportion to number of students.