To qualify for a special program at university, sharma had to write a standardized test. The test had a maximum score of 750, with a mean score of 540 and a standard deviation of 70. Scores on this test were normally distributed. Only those applicants scoring above the third quartile (the top 25%) are admitted to the program. Sharma scored 655 on this test. Will she be admitted to the program?

Question

To qualify for a special program at university, sharma had to write a standardized test. The test had a maximum score of 750, with a mean score of 540 and a standard deviation of 70. Scores on this test were normally distributed. Only those applicants scoring above the third quartile (the top 25%) are admitted to the program. Sharma scored 655 on this test. Will she be admitted to the program?

Answer 1

you can play around with Z table stuff here:

http://davidmlane.com/hyperstat/z_table.html

Answer 2

To determine whether Sharma will be admitted to the program, we need to compare her score of 655 with the scores of other applicants.

First, let's find the z-score of Sharma's score. The z-score measures how many standard deviations above or below the mean Sharma's score is. It is calculated using the formula:

z = (x - mean) / standard deviation

Substituting the given values, we have:

z = (655 - 540) / 70 ≈ 1.643

Next, we need to find the corresponding cumulative probability associated with Sharma's z-score. This cumulative probability represents the proportion of test-takers who scored below Sharma.

We can look up the cumulative probability in a standard normal distribution table or use a statistical calculator. For a z-score of 1.643, the cumulative probability is approximately 0.9492.

Since we are interested in the top 25% of scores, we need to calculate the threshold z-score that corresponds to the upper quartile. The upper quartile is equivalent to the 75th percentile or a cumulative probability of 0.75.

Again, referring to the standard normal distribution table or using a calculator, we can find that the z-score corresponding to a cumulative probability of 0.75 is approximately 0.6745.

Now, if Sharma's z-score of 1.643 is greater than the upper quartile z-score of 0.6745, it means that her score is above the third quartile and she will be admitted to the program. Otherwise, if her z-score is less than or equal to the upper quartile z-score, she will not be admitted.

In this case, 1.643 > 0.6745, which means Sharma's score of 655 is above the third quartile. Therefore, she will be admitted to the program.