Question

= 50 and standard deviation o = 7. Compute the probability. Be sure to draw a normal curve with Assume the random variable X is normally distributed with mean the area corresponding to the probability shaded. PIX> 36) Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to P(X> 36)? OA OB 36 50 36 50 36 50 PIX>36) = 0.6406 (Round to four decimal places as needed.)

Answer 1

Option (A) is the correct graph representing the area corresponding to P(X > 36). (Ans).

We have, X ~ N(50, 7) i.e. (X - 50)/7 ~ N(0,1)

So, P(X > 36) = 1 - P(X $\leq$ 36) = 1 - P[(X - 50)/7 $\leq$ (36 - 50)/7] = 1 - P[(X - 50)/7 $\leq$ -2] = 1 - $\Phi$(-2) = 1 - 0.0228 = 0.9772 (Ans).