The Normal Distribution Curve Which Models, Distributions of Data in a Wide

Multiple Choice

The normal distribution curve which models, distributions of data in a wide range of applications, is given by the function
$p ( x ) = \frac { 1 } { \sqrt { 2 \pi } } e ^ { - ( x - \mu ) ^ { 2 } / 2 \delta ^ { 2 } }$ where $\pi = 3.14159265 \ldots$ and $\sigma$ and $\mu$ are constants called the standard deviation and the mean, respectively. Its graph is shown in the figure. ?
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 $\mu = 4.1$ and $\sigma = 1.2$ . The percentage of consumers who gave the toothpaste a score between a and b on the section is given by $\int _ { a } ^ { b } p ( x ) d x$
Use a Riemann sum with n = 10 to estimate the percentage of customers who rated the toothpaste 5 or higher. (Use the range 4.5 to 10.5.) Round your answer to the nearest whole number.

A) 45%
B) 46%
C) 47%
D) 48%
E) 49%