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 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model.

Question

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 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as  Find the derivative of the model. ​

Quizplus · Accepted Answer

The normal probability density function is given by f(x) = (1/σ√(2π))e^(-(x-μ)^2/(2σ^2)), where μ is the mean and σ is the standard deviation. Taking the derivative with respect to x, we get: f'(x) = (-1/σ√(2π))e^(-(x-μ)^2/(2σ^2)) * (x-μ)/σ^2. Substituting the values given in the problem, we get f'(x) = (-1/11.5√(2π))e^(-(x-450)^2/(2*11.5^2)) * (x-450)/11.5^2. Simplifying, we get f'(x) = (-0.006938)(x-450)e^(-(x-450)^2/(2*11.5^2)). Therefore, the answer is B.

A Survey of High School Seniors from a Certain School