Let X denote the weight of an individual randomly selected from a town. Assume that X follows a normal distribution with mean=130 and variance= 25. Compute the probability that when we randomly choose someone from this town his/her weight measures more than 150

0

Step-by-step explanation:

Solution:-

- A random variable X denotes the weight of an individual randomly selected from a town

- Assuming X follows a normal distribution with mean u , and standard deviation sd.

                                   X ~ N ( u , sd )

                                   X ~ N ( 130 , 5^2 )

- We are to compute the the probability that when we randomly choose someone from this town his/her weight measures more than 150.

- We will first evaluate the Z-score value for the statistics:                                  

                                  P ( X > x ) = P ( Z > ( x - u ) /sd)

                                  P ( X > 150 ) = P ( Z > ( 150 - 130) / 5)

                                  P ( X > 150 ) = P ( Z > 4.0 )

- Now use standardized Z-look up tables and evaluate the probability P ( Z < 4 ) :

                                  P ( Z < 4 ) = 1.0

                                  P ( X > 150 ) = P ( Z > 4 ) = 1 - P ( Z < 4 )

                                  P ( X > 150 ) = 1 - 1 = 0