Question

the graph shows the distribution of weights (in pounds) of male duck - billed platypuses. the distribution is approximately normal, with a mean of 3.75 pounds and a standard deviation of 0.52 pounds. what percent of male duck - billed platypuses have a weight of between 2.71 and 4.79 pounds? 34% 68% 95% 99.7% male duck - billed platypuses 1.67 2.19 2.71 3.23 3.75 4.27 4.79 5.31 5.83 weight (pounds)

Explanation:

Step1: Calculate the number of standard deviations from the mean

For \(x_1 = 2.71\): \(z_1=\frac{2.71 - 3.75}{0.52}=\frac{- 1.04}{0.52}=- 2\)
For \(x_2 = 4.79\): \(z_2=\frac{4.79 - 3.75}{0.52}=\frac{1.04}{0.52}=2\)

Step2: Use the empirical rule for normal distribution

The empirical rule states that for a normal distribution:

• Approximately \(68\%\) of the data lies within \(z=\pm1\)
• Approximately \(95\%\) of the data lies within \(z = \pm2\)
• Approximately \(99.7\%\) of the data lies within \(z=\pm3\)

Since \(z=-2\) and \(z = 2\), by the empirical rule, approximately \(95\%\) of the data lies between these two \(z -\)scores.

Answer:

\(95\%\)