Question

In a national basketball association, the top free-throw shooters usually have probability of about 0.90 of making any given free throw. Complete parts a through c. a. During a game, one such player shot 11 free throws. Let X = number of free throws made. What must you assume in order for X to have a binomial distribution? A. It is assumed that the data are binary, that there is the same probability of success for each trial (free throw), and that the trials are dependent 8. It is assumed that the data are binary, that there is the same probability of success for each trial (free throw), and that the trials are independent. C. It is assumed that the data are binary, that probabilities of success for trials (free throws) differ for each trial, and that the trials are independent. D. It is assumed that the data are not binary. b. Specify the values of n and p for the binomial distribution of X in part a. n11 P = 0.90 (Type integers or decimals. Do not round.) c. Find the probability that the player made all 11 free throws, 10 free throws, and more than 8 free throws. The probability that the player made all 11 free throws is (Round to the nearest thousandth as needed.)

Answer 1

here this is binomial with parameter n=11 and p=0.9

c)

P(made all 11 ) =0.9^11 =0.314

P(made 10) =P(X=10)=

(nCx)px(1−p)(n-x)    =

0.384

P(more than 8) =P(X>=9)=1-P(X<=8)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.910