Question

The attendance at baseball games at a certain stadium is normally distributed, with a mean of 26,000 and a standard deviation of 1200. For any given game:

A) What is the probability that attendance is greater than 27,500?

B) What is the probability that attendance will be 26,000 or more?

C) What is the probability of attendance between 25,000 and 28,000?

D) What must the attendance be at the game, for that game's attendance to be in the top 10% of all games?

E) What is the probability that attendance is less than 23,000?

Answer 1

Answer:-

Given That:-

The attendance at baseball games at a certain stadium is normally distributed, with a mean of 26,000 and a standard deviation of 1200. For any given game:

Given

A)

What is the probability that attendance is greater than 27,500

=  

=  

=  

= 1 - 0.8943

= 0.1057

(B)

What is the probability that attendance will be 26,000 or more

=  

=  

= 1 - 0.5

= 0.5

(C)

What is the probability of attendance between 25,000 and 28,000

    

= 0.9522 - 0.2023

= 0.7499

(D)

What must the attendance be at the game, for that game's attendance to be in the top 10% of all games

10% = 0.10

P(X > X) = 0.10

By using Z table P(Z > 1.282) = 0.10

= Z_0.10 (1200) + 26000 by solving Z table Z_0.90 = 1.282

= 1.282(1200) + 26000

= 27538

(E)

What is the probability that attendance is less than 23,000

P(X < 23000)

  

  

= 0.9937