Answer to Question #265831 in Statistics and Probability for marc

Question

The average age of team managers is 35 years. Assume the variable is normally distributed. If the standard deviation is 5 years, find the probability that the age of a randomly selected team manager will be in the range between 25 and 40 years old.

 

Solution:

Step 1: Draw a figure and represent the area.

Step 2: Find the z value.

Step 3: Find the appropriate area. 

Answer 1

$\mu=35 \\ \sigma= 5 \\ P(25<X<40) = P(X<40) -P(X<25) \\ =P(Z< \frac{40-35}{5}) -P(Z< \frac{25-35}{5}) \\ = P(Z< 1) -P(Z< -2) \\ = 0.8413 -0.0227 \\ = 0.8186$