Question

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 73 and a standard deviation of 10. The professor has informed us that 7.5 percent of his students received A's while only 2.25 percent of his students failed the course and recelved F's. (You may need to use the appropriate appendix table or technology to answer this question.) (a) What is the minimum score needed to make an A?

Answer 1

To find the minimum score needed to make an A, we need to determine the z-score corresponding to the 7.5 percentile.

Step-by-step explanation:

To find the minimum score needed to make an A, we need to determine the z-score corresponding to the 7.5 percentile. Using the standard normal distribution table or a calculator, we can find that the z-score corresponding to the 7.5 percentile is approximately -1.405. We can then use the formula z = (x - μ) / σ, where z is the z-score, x is the score we want to find, μ is the mean, and σ is the standard deviation. Rearranging the formula, we can solve for x: x = z * σ + μ. Substituting in the values, x = -1.405 * 10 + 73 = 58.95. Therefore, the minimum score needed to make an A is approximately 59.