Question

In a normal distribution 9.85% of the values are under 40 and 89.97% of the values are under 60. Find the point of inflection of the distribution

Answer 1

$$P(Z<Z_1)=0.0985$$

$$Z_1=\frac{40-\mu}{\sigma}=-1.29$$

$$P(Z<Z_2)=0.8997$$

$$Z_2=\frac{60-\mu}{\sigma}=1.28$$

$$\frac{60-\mu}{40-\mu}=-\frac{1.28}{1.29}$$

$$\mu=50.0$$

Thus,

$$\frac{60-50}{\sigma}=1.28$$

$$\sigma=7.8$$

Points of inflection are

$$x=50-7.8=42.2$$

$$x'=50+7.8=57.8$$