Question

Find the value of x so that the area under the normal curve between μ and x is approximately 0.4800 and the value of x is greater than μ.

Answer 1

$$P(Z<\dfrac{x-\mu}{\sigma})-0.5=0.4800$$

$$P(Z<\dfrac{x-\mu}{\sigma})=0.9800$$

$$\dfrac{x-\mu}{\sigma}\approx2.053749$$

$$x\approx\mu+2.053749\sigma$$

Given $\mu=185, \sigma=18.$

$$x\approx185+2.053749(18)$$

$$x\approx221.967$$