Cold Streaks 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 he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 30% of the time he comes to the plate.
(a) Find and interpret the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming that at-bats are independent events. Hint: The hitter makes an out 70% of the time.
(b) Are cold streaks unusual?
(c) Find the probability the hitter makes five consecutive outs and then reaches base safely.
(d) Discuss the assumption of independence in consecutive at-bats.
Step 1 of 5) Cold Streaks 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 he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 30% of the time he comes to the plate. (a) Find and interpret the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming that at-bats are independent events. Hint: The hitter makes an out 70% of the time. (b) Are cold streaks unusual (c) Find the probability the hitter makes five consecutive outs and then reaches base safely. (d) Discuss the assumption of independence in consecutive at-bats. Comparing Two Sets of Data. Problem The data in Table 7 represent the IQ scores of a random sample of 100 students from two different universities. For each university, compute the mean IQ score and draw a histogram using a lower class limit of 55 for the first class and a class width of 15. Comment on the results.
