Given that the general population is normally distributed on a standard scale measuring math aptitude with Mean = 50 (s.d. = 10), approximately what percentage of the population has a math aptitude score between 40 and 60?

You need to find the z-score

(40 - 50)/10 = z

(60 - 50)/10 = z

So, you are looking for -1 and +1 standard deviations.

Find the area between -1 and +1 standard deviation by using a z-table or else by using the 65.. etc, rule.

68.2%

To find the percentage of the population with a math aptitude score between 40 and 60, we need to calculate the area under the normal curve between these two values.

Since the population is normally distributed with a mean of 50 and a standard deviation of 10, we can use the Z-score formula to standardize these values and find the corresponding Z-scores.

The Z-score formula is:
Z = (X - μ) / σ,

where Z is the standard score, X is the raw score, μ is the mean, and σ is the standard deviation.

For X = 40:
Z1 = (40 - 50) / 10 = -1

For X = 60:
Z2 = (60 - 50) / 10 = 1

Now, we need to find the area between these two Z-scores using a normal distribution table or a calculator.

Looking up the Z-scores in the standard normal distribution table, we find:
P(Z < -1) = 0.1587 (probability of a score less than -1)
P(Z < 1) = 0.8413 (probability of a score less than 1)

Since we want to find the area between these two Z-scores, we subtract the probability of Z < -1 from the probability of Z < 1:
P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826

Therefore, approximately 68.26% of the population has a math aptitude score between 40 and 60.