Question

1. the scores for oklahomas peace officer standards and training test are normally distributed as shown in the normal curve below where test scores range from 0 to 100.

normal curve image with x - axis: 19, 31, 43, 55, 67, 79, 91, labeled test scores
the data is normally distributed with a mean of dropdown and a standard deviation of dropdown. about dropdown of the people taking the test score between 43 and 67.

Explanation:

Step1: Find the mean

In a normal distribution, the mean is at the center of the curve. Looking at the x - values (19, 31, 43, 55, 67, 79, 91), the middle value is 55. So the mean ($\mu$) is 55.

Step2: Find the standard deviation

To find the standard deviation ($\sigma$), we look at the distance between consecutive values. Let's take the distance from the mean (55) to the next value. 55 - 43 = 12, 67 - 55 = 12, 43 - 31 = 12, 31 - 19 = 12, 79 - 67 = 12, 91 - 79 = 12. So the standard deviation is 12.

Step3: Find the percentage between 43 and 67

We know that in a normal distribution, the empirical rule (68 - 95 - 99.7 rule) states that about 68% of the data is within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
The value 43 is $\mu-\sigma=55 - 12 = 43$ and 67 is $\mu+\sigma=55 + 12 = 67$. So the data between 43 and 67 is within 1 standard deviation of the mean. By the empirical rule, about 68% of the data lies within 1 standard deviation of the mean.

Answer:

Mean: 55, Standard Deviation: 12, Percentage: 68%