Concept explainers
Joe Record. One of longest-standing records
in sports is the 56-game hitting streak (in baseball) Joe Dimaggio.
Assume that a player on a long •hot streak- is bat-
ting. 400. which is abotut the best that anyone ever hits over a
period of 50 or more games (A batting average of .400 means the
batter gets a hit 40% of the time. Typically, only a handful of
players each year hit that well for a long 56 games.)
a. What is the probability that a player batting -400 will get at
least one hit in four at-bats?
b. Use the result in part (a) to calculate the probability Of
a hitter getting a hit in one stretch of 56 consecutive
assuming four at-bats per game.
c. suppose that, instead Of batting .400. a player has a more
ordinary average 0f .300. In that case, what is the probability
of the player getting a hit in one stretch of 56 consecutive
Vines, assuming four at-bats per game?
d. Considering the results in parts (b) and (c) and the fact
that baseball has been played for about 100 years. are you
surprised that someone a record Of hitting in 50 consecu-
tive games? Explain clearly.
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