Question

Given the following normal distribution what is the probability X>35. That is, P(X>35). Assume standard deviation σ=6.

Answer 1

If $X\sim N(\mu, \sigma^2),$ then

$$Z={X-\mu\over \sigma}\sim N(0, 1)$$

Given $\mu=37, \sigma=6.$

$$P(X>35)=1-P(X\leq35)=$$

$$=1-P(Z\leq{35-37\over 6})\approx1-P(Z\leq-0.333333)\approx$$

$$\approx1-0.369441=0.630559$$