A math professor notices that scores from a recent exam are normally distributed with a mean of 64 and a standard deviation of 5. Answer the following questions using integer values. The professor decides to grade on a curve. If he wants 0.15% of the students to get an A, what is the minimum score for that A?

Again, I would appreciate seeing how this was solved.

Thanks

Given estimates and specifications that the population standard deviations is 250, total precision is 100 and the researcher wishes to be 95% confident in the result, the require sample size is?

It shows there has been a response to my question but I don't see one that in my opinion addresses my question.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and its corresponding Z score.

Z = (score-mean)/SD

Put values into the above equation to find the score.

First, if you have a question, it is much better to put it in as a separate post in <Post a New Question> rather than attaching it to a previous question, where it is more likely to be overlooked.

Second, I am not familiar with your term, "total precision." Try posting again with clearer terms.

To find the minimum score for an A, we need to determine the score that corresponds to the 0.15th percentile of the distribution. This is the value below which only 0.15% of the scores fall.

The first step is to find the z-score associated with the desired percentile. The z-score measures how many standard deviations a value is from the mean in a normal distribution. We can calculate the z-score using the formula:

z = (X - μ) / σ

Where:
X = Score
μ = Mean (64)
σ = Standard deviation (5)

To find the z-score for the 0.15th percentile, we need to find the z-score that corresponds to the cumulative probability of 0.15%. This can be done using statistical tables or a standard normal distribution calculator.

Using the tables or calculator, we find that the z-score corresponding to a cumulative probability of 0.15% is approximately -2.964.

Now, we can rearrange the formula to solve for X:

X = z * σ + μ

Plugging in the values, we get:

X = (-2.964) * 5 + 64

Calculating it:

X ≈ -14.82 + 64 ≈ 49.18

Therefore, the minimum score for an A is approximately 49.