Question

Suppose that during practice, a basketball player can make a free throw 85% of the time. Furthermore, assume that a sequence of free-throw shooting can be thought of as independent Bernoulli trials. Let X be the minimum number of free throws that this player must attempt to make a total of ten shots.

(a) What is the expected value and variance of X? Show your work.

(b) What is the probability that the player must attempt 15 or fewer shots in

order to make ten? Show your work.

Answer 1

Given P- 95% = 0.85 4:10 L'S number of success a) Expected value of x E(X) x 10 0.85 5/11376 variance Of X vex): a clap) p2 10 x (-0.85) 0.85 = 2.49 q=1-P=1-0.85 -0.015 b) p(player must attempt 15 or fever) P(x415) Ža) fc.cis) 7-10 10 X 0.85 1-10 P(X=10) + P(x-11) + P(x=0)) + PC413 +PCX16) + f(x=15) ( x 0.85" x 0.959) + (,XC-85"kocis") + ("qxos"icos?) *("<,^0.5**0.015) +(126, 40-85"x0.css')+('eq xo58s " XO-CIS + 0.0024 +0.00015 + 0.00 0007 = 0.1969 + 0.0295 + 0-0000003 50.229 P(x – 15) - 6-2240