Question

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find P81, which separates the bottom 81% from the top 19%. Round to two decimal places. A. 0.29 B. 0.88

Answer 1

To find P81, we need to find the z-score corresponding to the bottom 81% of the distribution. The z-score is approximately 0.91, and the corresponding raw score is approximately 73.73. Therefore, the correct answer is A. 0.29.

Step-by-step explanation:

To find P81, which separates the bottom 81% from the top 19%, we need to find the z-score corresponding to the bottom 81% of the distribution. We can use the z-score formula:

z = (x - mean) / standard deviation

For the bottom 81%, we need to find the z-score that corresponds to a cumulative probability of 0.81. Using a standard normal distribution table or calculator, we can find that the z-score is approximately 0.91.

To find the corresponding raw score (x), we can rearrange the z-score formula:

x = z x standard deviation + mean

Using the given mean of 63.2 and standard deviation of 11.7, we can calculate:

x = 0.91 x 11.7 + 63.2 = 73.73

So P81 is approximately 73.73. Therefore, the correct answer is A. 0.29.