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?
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.