The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15.(a) Let X be a person's IQ score. Write the formula for the density function of IQ scores.p(x)=(b) Estimate the fraction of the population with IQ between 120 and 125.fraction =

Answer:4.4% of the population with IQ between 120 and 125. Step-by-step explanation:We are given the following information in the question:Mean, μ = 100Standard Deviation, σ = 15We are given that the distribution of IQ scores is a bell shaped distribution that is a normal distribution.a) Let X be a person's IQ score. Then, density functions for IQ scores is given by:[tex]P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{z^2}{2}}\\\\\text{where,}\\\\z = \frac{x-\mu}{\sigma}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-100)^2}{450}}[/tex]b) P(population with IQ between 120 and 125.)Formula:[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex][tex]P(120 \leq x \leq 125) = P(\displaystyle\frac{120 - 100}{15} \leq z \leq \displaystyle\frac{125-100}{15}) = P(1.33 \leq z \leq 1.66)\\\\= P(z \leq 1.66) - P(z < 1.33)\\= 0.952 - 0.908 = 0.044 = 4.4\%[/tex][tex]P(120 \leq x \leq 125) = 4.4\%[/tex]