Question

common assessment 1 advanced algebra

1. the weights of fish were measured in kg from a certain lake. the graph below shows that the weights have a normal distribution.

about what percent of the fish are between 14 and 26 kg?
a. 68%
b. 81.5%
c. 47.5%
d. 95%

Explanation:

Step1: Recall the empirical rule of normal distribution

In a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean ($\mu\pm\sigma$), about 95% of the data lies within 2 standard deviations of the mean ($\mu\pm2\sigma$), and about 99.7% of the data lies within 3 standard deviations of the mean ($\mu\pm3\sigma$). If the mean $\mu = 22$ and we assume the standard deviation $\sigma = 4$ (since $22 - 14=8$ and $26 - 22 = 4$, and $8 = 2\times4$), the values 14 and 26 are 2 standard - deviations away from the mean ($22-2\times4 = 14$ and $22 + 2\times4=26$).

Step2: Determine the percentage of data

According to the empirical rule, the percentage of data within $\mu\pm2\sigma$ is 95%.

Answer:

d. 95%