Question

esteban measured the lengths of a species of bird in a region. the graph below shows that the measured lengths form a normal distribution.

about what percent of the bird population is between 22 and 26 cm long?

a. 17%
b. 27%
c. 34%
d. 50%

Explanation:

Step1: Recall empirical rule for normal distribution

In a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean, about 95% lies within 2 standard deviations of the mean, and about 99.7% lies within 3 standard deviations of the mean. If the distribution is symmetric, half of the data lies on each side of the mean.

Step2: Analyze the range

Assume the mean is at the center of the normal - distribution curve. If we consider the range from the mean to 1 standard deviation above the mean, the proportion of data in this range is about 34%. Similarly, the range from the mean to 1 standard deviation below the mean also has about 34% of the data.
If the range from 22 to 26 is symmetric around the mean (assuming a normal distribution), and we know that the range from the mean to a certain value within 1 standard - deviation has 34% of the data, and if 22 and 26 are symmetric about the mean, the proportion of data between 22 and 26 is about 34% + 34%=68% if they are 1 standard - deviation away from the mean on either side. But if we assume a more general case where we consider the fact that the normal distribution is symmetric and we are looking at a range that is likely within 1 standard - deviation of the mean on both sides, the closest value among the options is 34% when we consider just one - side of the mean within the given range.

Answer:

C. 34%