Question

For a population with a μ=52 and σ=1.35, a. what is the z-score corresponding to X=54 ? b. what proportion of scores are between 54 and 56?p= c. The proportions from the table used to find this answer are and

Answer 1

To calculate the z-score for a score of 54 in a population with a mean of 52 and standard deviation of 1.35, subtract the mean from the score and divide by the standard deviation, resulting in a z-score of approximately 1.48. To find the proportion of scores between two points, determine the z-scores for both and refer to a standard normal distribution table for the cumulative probabilities.

Step-by-step explanation:

Finding a z-score & Understanding Proportions in a Normal Distribution

To find the z-score corresponding to X=54 for a population with a mean (μ) of 52 and a standard deviation (σ) of 1.35:

Z = (X - μ) / σ

Z = (54 - 52) / 1.35

Z = 2 / 1.35

Z ≈ 1.48

The z-score of about 1.48 indicates how many standard deviations the score of 54 is from the mean.

To find the proportion of scores between X=54 and X=56, you would need to look up the corresponding z-scores for these values in the standard normal distribution table (often found in statistics textbooks or online resources).

Once you have the two z-scores, you can determine the proportion of scores between them by finding the difference of the cumulative probabilities corresponding to these z-scores. The specific proportions will depend on the z-scores and the standard normal distribution table used.