Players in sports are said to have \"hot streaks\" and \"cold streaks.\" For exa
ID: 3303460 • Letter: P
Question
Players in sports are said to have "hot streaks" and "cold streaks." For example, a batter in baseball might be considered to be in a slump, or cold streak, if that player has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 38% of the time he comes to the plate. Complete parts (a) through (c) below.
Find the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming at-bats are independent events. Hint: The hitter makes an out 62% of the time.
a. P(hitter makes 10 consecutive outs) =
b. Are cold streaks unusual?
c. Interpret the probability from part a.
In repeated sets of 10 consecutive at-bats, the hitter is expected to make an out in all 10 at-bats about 18 times out of 1000.
Explanation / Answer
from binomial distribution:
a) P(hitter makes 10 consecutive outs) = (1-0.38)10 =0.0084
b) Yes as probability of that is less then 0.05.
c) In repeated sets of 10 consecutive at-bats, the hitter is expected to make an out in all 10 at-bats about 8 times out of 1000