A Survey of High School Seniors from a Certain School $f ( x ) = \frac { 1 } { 13.5 \sqrt { 2 \pi } } e ^ { - ( x - 700 ) ^ { 2 } /3 64.5 }$

question 69

Multiple Choice

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 700 with a standard deviation of 13.5. By a normal probability density function the data can be modeled as $f ( x ) = \frac { 1 } { 13.5 \sqrt { 2 \pi } } e ^ { - ( x - 700 ) ^ { 2 } /3 64.5 }$ . Find the derivative of the model.

• A) \(f ^ { \prime } ( x ) = \frac { - 2 \sqrt { 2 } ( x - 700 ) e ^ { - ( x -700 ) ^ { 2 } / 182.25 } } { 4,921 \sqrt { \pi } }\)
• B) \(f ^ { \prime } ( x ) = \frac { - 2 \sqrt { 2 } ( x - 700 ) e ^ { - ( x -700 ) ^ { 2 } / 364.5 } } { 9,842 \sqrt { \pi } }\)
• C) \(f ^ { \prime } ( x ) = \frac { \sqrt { 2 } ( x - 700 ) e ^ { - ( x - 700 ) ^ { 2 } / 364.5 } } { 4,921 \sqrt { \pi } }\)
• D) \(f ^ { \prime } ( x ) = \frac { \sqrt { 2 } ( x - 700 ) e ^ { - ( x - 700 ) ^ { 2 } / 364.5 } } { 9,842 \sqrt { \pi } }\)
• E) \(f ^ { \prime } ( x ) = \frac { \sqrt { 2 } ( x - 700 ) e ^ { - ( x - 70 ) ^ { 2 } / 182.25 } } { 4,921 \sqrt { \pi } }\)

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Definitions:

Sign Stimulus

An external sensory cue that triggers a specific innate behavior in animals and humans.

Instincts

Innate, biologically determined behavior patterns common to all members of a species that are exhibited by all individuals in the absence of learning or experience.

Physiological State

The condition of the body or bodily functions at a given time, taking into account both internal and external factors.

Homeostasis

The body’s tendency to maintain an equilibrium, or steady state.