Chapter 13.3, Problem 72E

(a)

To determine

To calculate: The percentage of consumers rated the toothpaste $5$ or above by using Riemann sum and use technology with $n=10$, if the percentage of consumers rated between a and b is given by ${\displaystyle \underset{a}{\overset{b}{\int }}p\left(x\right)dx}$ where $p\left(x\right)$ is the distribution of the data in a wide range of application is given by $p\left(x\right)=\frac{1}{\sqrt{2\pi \sigma }}{e}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}$ is shown in the following graph, standard deviation $\sigma$ is $1.0$ and mean $\mu$ is $4.5$.

(b)

To determine

To calculate: The percentage of consumers rated the toothpaste $0$ or $1$ by using Riemann sum and use technology with $n=10$, if the percentage of consumers rated between a and b is given by ${\displaystyle \underset{a}{\overset{b}{\int }}p\left(x\right)dx}$ where $p\left(x\right)$ is the distribution of the data in a wide range of application is given by $p\left(x\right)=\frac{1}{\sqrt{2\pi \sigma }}{e}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}$ is shown in the following graph, standard deviation $\sigma$ is $1.0$ and mean $\mu$ is $4.5$.