Question

Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. with the distribution of 0.55

Answer 1

$$P(X>x)=0.55$$

The z-score of a normally distributed random variable, X, with mean μ and standard deviation σ, at the point x, is given as:

$$Z={X-\mu \over \sigma}$$

$$P(X\leq x)=1-P(X>x)=1-0.55=0.45$$

$$P(Z\leq {x-\mu \over \sigma})=0.45=>{x-\mu \over \sigma}\approx-0.12566$$

$$x\approx15(-0.12566)+100\approx98.1151$$

$x\approx98.1$