A basketball player has made 83% of his foul shots during the season. Assume the shots are independent. a) What's the expected number of shots until he misses? b) If the player shoots 16 foul shots in the fourth quarter, how many shots do YOU expect him to make? c) What is the standard deviation of the 16 shots? a) The player is expected to make 6 shots before his first miss (Round to the nearest whole number as needed). b) The player is expected to make 13 shots in the fourth quarter (Round to the nearest whole number as needed). c) The standard deviation of the 16 shots is 1.50 (Round to two decimal places as needed).
Added by Jose Luis B.
Step 1
Given that the player has made 83% of his foul shots, the probability of making a shot is 0.83 and the probability of missing a shot is 0.17. The expected number of shots until he misses can be calculated as 1 / 0.17 = 5.88, which rounds to 6 shots. Show more…
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A basketball player has made 80$\%$ of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight's game he a) misses for the first time on his fifth attempt. b) makes his first basket on his fourth shot. c) makes his first basket on one of his first 3 shots.
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Sri K.
Jerry Stackhouse of the National Basketball Association's Dallas Mavericks is the best free- throw shooter on the team, making 89$\%$ of his shots (ESPN website, July, $2008 ) .$ Assume that late in a basketball game, Jerry Stackhouse is fouled and is awarded two shots. $\begin{array}{l}{\text { a. What is the probability that he will make both shots? }} \\ {\text { b. What is the probability that he will make at least one shot? }} \\ {\text { c. What is the probability that he will miss both shots? }}\end{array}$ $\begin{array}{l}{\text { d. Late in a basketball game, a team often intentionally fouls an opposing player in }} \\ {\text { order to stop the game clock. The usual strategy is to intentionally foul the other team's }} \\ {\text { worst free-throw shooter. Assume that the Dallas Mavericks' center makes } 58 \% \text { of his }}\end{array}$ free-throw shots. Calculate the probabilities for the center as shown in parts (a), (b), (b), and $(\mathrm{c}),$ and show that intentionally fouling the Dallas Mavericks' center is a better strategy than intentionally fouling Jerry Stackhouse.
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