Question

Find the following probabilities if the random variable X is normally distributed with

mean 15 and standard deviation 3.

(i) P(X<10)

(ii) P(10<X<25 )

Given that Z is a standard normal random variable, find z for each situation,

(i) The area to the left of Z is 0.2115

(ii) The area to the right of Z is 0.5000

Answer 1

1.

(i)

$$P(X<10)=P(Z<\dfrac{10-15}{3})\approx0.047790$$

(ii)

$$P(10<X<25)=P(Z<\dfrac{25-15}{3})$$

$$-P(Z\le\dfrac{10-15}{3})\approx0.9995709-0.0477904$$

$$\approx0.951781$$

2.

(i)

$$P(Z<z)=0.2115$$

$$z=-0.801227$$

(ii)

$$P(Z>z)=0.5000$$

$$z=0$$