Answer to Question #340555 in Statistics and Probability for joshipoo

Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

𝜇 = 4; 𝜎 = 2

P(3 ≤ x ≤ 6) = 

Answer 1

$$P(3\le X\le 6)=P(Z\le\dfrac{6-4}{2})-P(Z<\dfrac{3-4}{2})$$

$$=P(Z\le1)-P(Z<-0.5)$$

$$\approx0.84134-0.30854\approx0.5328$$