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%

Explanation:

Step1: Calculate the difference from the mean

For \(2.71\): \(3.75 - 2.71=1.04\). For \(4.79\): \(4.79 - 3.75 = 1.04\).

Step2: Divide by the standard deviation

\(\frac{1.04}{0.52}=2\). So \(2.71=\mu - 2\sigma\) and \(4.79=\mu + 2\sigma\) (where \(\mu = 3.75\) is the mean and \(\sigma=0.52\) is the standard deviation).

Step3: Apply the empirical rule

The empirical rule (68 - 95 - 99.7 rule) states that for a normal distribution, approximately \(95\%\) of the data lies within \(\mu\pm2\sigma\).

Answer:

95%