The Normal Distribution Curve, Which Models the Distributions of Data $p ( x ) = \frac { 1 } { \sqrt { 2 \pi } \sigma } e ^ { \frac { - ( x - \mu ) ^ { 2 } } { 2 \sigma ^ { 2 } } }$

question 113

Multiple Choice

The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function $p ( x ) = \frac { 1 } { \sqrt { 2 \pi } \sigma } e ^ { \frac { - ( x - \mu ) ^ { 2 } } { 2 \sigma ^ { 2 } } }$ , $\pi = 3.14159265 \ldots$ and and are constants called the standard deviation and the mean, respectively. With $\sigma = 3$ and $\mu = 5$ , approximate $\int _ { - \infty } ^ { \infty } p ( x ) \mathrm { d } x$ .

• A)3
• B) -5
• C) 5
• D) -1
• E) 1

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Definitions:

Delta Connected Motor

A method of connecting a three-phase motor where the ends of each coil are connected in a triangle or delta configuration, allowing for the use of a high voltage network.

High Voltage

Refers to electric potential at a level high enough to pose a hazard to humans, typically classified as more than 1000 volts in alternating current (AC) or 1500 volts in direct current (DC).

Capacitor-start

A motor design that includes a capacitor in the starting circuit for improved startup torque, commonly used in single-phase AC motors.

Capacitor-run Motors

Electric motors that use a capacitor in their circuit for the purpose of running efficiently, often found in HVAC systems and smaller machinery.