The average score of local students on a college entrance exam is 110 with standard deviation of 15. The distribution is roughly bell-shaped. What is the percentage of local student with score below 95? Use the empirical rule to find the following percentage. A. 34%
B. 16%
C. 15.5%
D. 13.5%

B

Step-by-step explanation:

Here, we want to use the empirical rule to find the percentage.

The first thing we will do here is to find the z-score

Mathematically;

z-score = (x -mean)/SD

from the question, x = 95, mean = 110

and SD = 15

So z-score will be ;

(95-110)/15 = -15/15 = -1

So the probability we want to calculate is;

P(z < -1)

In terms of the empirical rule, we want to find the proportion of the scores which is less than 1 standard deviation of the mean.

According to the empirical rule, the proportion which is less than 1 standard deviation below the mean is 15.866% and the closest answer to this is 16% which is option B

By definition, the empirical rule is basically used in finding the proportion of values in this case scores which are at a certain standard deviation value below or above the mean. Below the mean are represented as negatives while above the mean are represented as positives.

step-by-step explanation:

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (