Question

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 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.

Step2: Identify the number of standard - deviations

If the mean is \(\mu = 20\) (assumed as the middle value of the normal distribution graph) and the standard deviation \(\sigma = 3\) (since \(20 - 14=6\) and \(26 - 20 = 6\), and \(6\div2 = 3\)), then \(14=\mu - 2\sigma\) and \(26=\mu+2\sigma\).

Step3: Apply the empirical rule

Since the values 14 and 26 are 2 standard deviations away from the mean, about 95% of the data lies between them.

Answer:

d. 95%