Questions: The normal distribution curve, which models the distribution of data in a wide range of applications, is given by the function p(x) = 1 / sqrt(2 π) e^(-(σ-μ)^2 / 2 s^2) where π = 3.14159265... and σ and μ are constants called the standard deviation and the mean, respectively. In a survey, consumers were asked to rate a new toothpaste on a scale of 1-10. The resulting data are modeled by a normal distribution with μ = 4.3 and σ = 1.1. The percentage of consumers who gave the toothpaste a score between a and b on the survey is given by ∫ from a to b p(v) dx. Use a Riemann sum with n = 10 to estimate the percentage of customers who rated the toothpaste 7 or higher. (Use the range 6.5 to 10.5.) Round to the nearest integer.

Transcript text: The normal distribution curve, which models the distribution of data in a wide range of applications, is given by the function $p(x)=\frac{1}{\sqrt{2 \pi}} e^{-(\sigma-\mu)^{2} / 2 s^{2}}$ where $\pi=3.14159265 . .$. and $\sigma$ and $\mu$ are constants called the standard deviation and the mean, respectively. In a survey, consumers were asked to rate a new toothpaste on a scale of 1-10. The resulting data are modeled by a normal distribution with $\mu=4.3$ and $\sigma=1.1$. The percentage of consumers who gave the toothpaste a score between $a$ and $b$ on the survey is given by $\int_{a}^{b} p(v) d x$. Use a Riemann sum with $n=10$ to estimate the percentage of customers who rated the toothpaste 7 or higher. (Use the range 6.5 to 10.5.) Round to the nearest integer.