Question

9.14 A baseball player has a batting average of 0.328. Let X be the number of hits the player gets during 20 times at bat. Use the central limit theorem to find the approximate probability P(X<k) for k = 1, 3, 6. Compare with the exact probability for each k.
Please use the central limit theorem.

Answer 1

ANSWER Given that * A baseball player has a batting average p'= 0.328. * Let it be the number of hits the player gets during n's 20 times * approximate probability use the Central limit theorem P(xck) for k = 1,316 . P=0.328 D = 20 * Mean - n.P 520x0328 26.58 * Standard deviation -fn.pl-P). 20x0.328 (1-0.328) = 16.5660.672) = 2.10

1-6.5 PIXS 1) = P(24 - ) = Plzs 15:52 = P( Z22.65) =0.996 P(x-3) = P(Z < 3-4.0) =P [241.70) = 0.9554 Plxs 6) = P(Z < 6-6.56) - P(Z30:27) = 0.3996