Question

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

Answer 1

0

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