The attendance at baseball games at a certain stadium is normally distributed, w

Question

The attendance at baseball games at a certain stadium is normally distributed, with a mean of 25, 000 and a standard deviation of 1200. For any given game: A) What is the probability that attendance is greater than 22, 500? B) What is the probability that attendance will be 25, 000 or more? C) What is the probability of attendance between 23, 500 and 27, 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 26, 000?

Explanation / Answer

Solution:-

Given = 25000 and = 1200 we have,

(a) P ( X > 22500 ) = P ( X > 22500 25000 ) = P ( X / > 22500 25000 / 1200)

Since Z = x / and 22500 25000 / 1200 = 2.0833 we have:

P ( X > 22500 ) = P ( Z > 2.083 )

Using the standard normal table to conclude that:

P (Z > 2.083) = 0.9814

(b) P(X > 25000) = 0.5

(c) P(23500 < X < 27000) = 0.8466

(d) Number of atendence at the game, such that it has 0.10 (10%) as probability.

Re-arranging and using the formula as in part (a) , X = 23,462

(e) P(X < 26000) = 0.7977

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