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 10 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 not binary.

B.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.

C. 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.

D.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.

b. Specify the values of n and p for the binomial distribution of X in part a.

n

=

1010

p

=

. 90.90

​(Type integers or decimals. Do not​ round.)

c.Find the probability that the player made all 10 free​ throws, 9 free​ throws, and more than 7 free throws. The probability that the player made all 10 free throws is 0.3870.387.

​(Round to the nearest thousandth as​ needed.)

The probability that he made 9 free throws is 0.3870.387.

​(Round to the nearest thousandth as​ needed.)

The probability that he made more than 7 free throws is 0.9470.947. ​(Round to the nearest thousandth as​ needed.)

Answer 1

solution - (a) het X = number made Then of free throws the assumptions distribution for to a binomial are D) It is assumed that the data are binary, that there is the same probability of success for each trial ( free throw) and the trials independent are b) n-x N=10 b = 0.90 X~B(n, p) Then P(x=x] "Cx p * (1-P)" x=0, 1, 2,--,h CC) Prob that the player made all io free throwes is given by P(x= 10) 10c10 (0.9) (6.1) 1 X (0.9)'" x 1 10-10 0.3488 ~ 0.349 he made 9 free throws is Prob that given by Plx=9] - 10 Cg (0.g) 3 x(0:1) 10-3 = 10x (0.99 Xool 0.387

more given Prob that he made them 7 free throws is by Plx>77 = P(x=8] +P/x=8] + P(x=10] 10Gq (0.9)% (0.1) + 0.349 + 0-387 = 458 6.98 x 0.01 +0.349 +0.387 = 0: 1937 to.349 +0.387 11 0.9297 0.930
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