Question

use the graph to complete the following. the probability that a boxer weighs between 60 and 80 pounds is 95 % complete p(x ≤ 65 pounds) = % done μ = 70 σ = 5 55 60 65 70 75 80 85

Explanation:

Step1: Recall Normal Distribution Properties

In a normal distribution with mean $\mu = 70$ and standard deviation $\sigma = 5$, we use the empirical rule (68 - 95 - 99.7 rule) and symmetry. The value 65 is $\mu - \sigma$ (since $70 - 5 = 65$).

Step2: Determine Probability for $x \leq 65$

The normal distribution is symmetric about $\mu$. The area to the left of $\mu$ is 50%. The area between $\mu - \sigma$ and $\mu$ is 68%/2 = 34% (by empirical rule, 68% within $\mu \pm \sigma$). So the area to the left of $\mu - \sigma$ (65) is $50\% - 34\% = 16\%$.

Answer:

16