use the graph to complete the following. the probability that a boxer weighs between 60 and 80 pounds is 95…
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
Answer
Explanation:
Step1: Calculate z - score
The z - score formula is $z=\frac{x-\mu}{\sigma}$. Here, $x = 65$, $\mu=70$, and $\sigma = 5$. So $z=\frac{65 - 70}{5}=\frac{- 5}{5}=-1$.
Step2: Use the empirical rule
The empirical rule for a normal distribution states that about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), about 95% lies within 2 standard - deviations of the mean ($\mu\pm2\sigma$), and about 99.7% lies within 3 standard - deviations of the mean ($\mu\pm3\sigma$). The area to the left of $z=-1$ is $\frac{100 - 68}{2}+34 = 16+34=16%$.
Answer:
16