Question

In 2018 there were 2416 major League baseball games. The mean attendance was 28837 with a standard deviation of 10853. Let us assume that the attendance in any game is independent from the attendance in any other game. Suppose, we randomly select 289 games, with replacement, from the list of 2416 games and look at the attendance for each game selected. Let M be the random variable representing the mean attendance of the selected games. Let T = the random variable representing the total attendance of the selected games. a) What theorem will let us treat T and Mas normal random variables? Chebychev's Theorem Central Limit Theorem Convolution Theorem Monte Carlo Theorem Law of Large Numbers b) What is the expected value of T? c) What is the standard deviation of T? d) If TH is T measured in thousands (e.g. 30000 = 30), then what is the standard deviation of TH e) What is the approximate probability that T in feet) is greater than 8,000,000? f) What is the standard deviation of M? g) What is the approximate probability M is between 28000 and 29000 feet? h) What is the approximate probability that I is within 2 standard deviations of its expected value?

Answer 1

a) Central Limit Theorem

b) E(T) = 28837*289 = 8333893

c)

Var(T) = 02.n → S.D.(T) = 0 n = 10853 289 = 184501

d) If we convert the units to thousands then the standard deviation will also change by thousand units because in standard deviation we take the square root after taking the differences from the mean.

S.D.(TH) = Othyn = 10.853 289 = 184.501