In a national basketball association, the top free-throw shooters usually have p

Question

In a national basketball association, the top free-throw shooters usually have probability of about 0.85 of making any given free throw. Complete parts (a) through (c) a. During a game, one such player shot 10 free throws. Let X- number of free throws made. What must you assume in order for X to have a binomial distrbution? A It is assumed that the data are binary, that probabilities of success for trials (free throws)differ for each trial, and that tha tials are Independent OB. 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 aro dependent. is assumed that the data are binary, that there is the same probability of success for each trial (free throw), and that the tials are independent Vc. It D. It is assumed that the data are not binary. b. Specity the values of n and p for the binomial distribution of X in (o n10 p= 085 c. Find the probability that the player made all 10 free throws and the probability that he made 9 free thros The probability that the player made all 10 free throws Round to the nearest hundredth as needed.)

Explanation / Answer

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

n = 10
p = 0.85

P(T9) = P(X = 9) = 10C9 * 0.85^9 * (1-85)^1 = 0.3474
P(T10) = P(X = 10) = 10C10 * 0.85^10 * (1-85)^0 = 0.1969

P(T10 | T9) = 0.1969/0.3474 = 0.5668

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