An aptitude test has a mean of 300 and a standard deviation of 40. The test scores are normally distributed. If 1000 people take the test, find the number of people who will score between 280 and 360.

http://davidmlane.com/hyperstat/z_table.html

To find the number of people who will score between 280 and 360 on the aptitude test, we need to calculate the z-scores corresponding to these scores and use the standard normal distribution table or statistical software.

Step 1: Calculate the z-scores for the given scores.
The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.

For the lower score of 280:
z1 = (280 - 300) / 40 = -0.5

For the upper score of 360:
z2 = (360 - 300) / 40 = 1.5

Step 2: Look up the probabilities associated with these z-scores.
Using a standard normal distribution table or statistical software, find the probability corresponding to each z-score.

The probability corresponding to z1 = -0.5 is 0.3085.
The probability corresponding to z2 = 1.5 is 0.9332.

Step 3: Calculate the number of people between these scores.
The number of people who will score between 280 and 360 is equal to the difference between the cumulative probabilities obtained from the standard normal distribution table.

Number of people = Probability(z1 < Z < z2) * Total number of people

Probability(z1 < Z < z2) = Probability(Z < z2) - Probability(Z < z1)

Using the cumulative probabilities obtained from the standard normal distribution table:

Probability(Z < z2) = 0.9332
Probability(Z < z1) = 0.3085

So, Probability(z1 < Z < z2) = 0.9332 - 0.3085 = 0.6247

Now, multiply this probability by the total number of people taking the test:

Number of people = 0.6247 * 1000
Number of people = 624.7

Therefore, approximately 625 people will score between 280 and 360 on the aptitude test.