Question

If x is a standard normal variate find the following probabilities by using normal probability i) p(0.87<x<1.28)

ii) p(-0.34<x<0.62)

iii) p(x>0 85)

iv)p(x>-0.65)

Answer 1

i)

$$P(0.87<x<1.28)=P(x<1.28)-P(x\leq 0.87)$$

$$\approx0.8997274-0.8078498\approx0.091878$$

ii)

$$P(-0.34<x<0.62)=P(x<0.62)-P(x\leq -0.34)$$

$$\approx0.7323711-0.3669283\approx0.365443$$

iii)

$$P(x>0.85)=1-P(x\leq 0.85)$$

$$\approx0.197663$$

iv)

$$P(x>-0.65)=1-P(x\leq -0.65)$$

$$\approx0.742154$$