Question

A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What percent of scores are between 42 and 58?

Answer 1

We can use the normal distribution to solve this problem. First, we need to standardize the scores using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

For the score of 42, z = (42 - 50) / 4 = -2. For the score of 58, z = (58 - 50) / 4 = 2.

We can use a standard normal distribution table to find the area under the curve between z = -2 and z = 2. This area represents the percentage of scores between 42 and 58.

From the table, we find that the area between z = -2 and z = 2 is approximately 0.9545. Therefore, approximately 95.45% of scores are between 42 and 58.