Question

PROBLEM 4. A baseball pitcher is known to throw strikes with a 75% probability. (Round answers to 4 decimal places.) (A) What is the most likely number of strikes the pitcher would throw out of 100 pitches? (Give formula and value.) (B) What is the probability of her throwing exactly that number of strikes? (Give formula and value.) (C) What is the standard deviation of the number of strikes the pitcher would throw out of 100? (Give formula and value.) (D)) Find the "usual range of the number of strikes we should expect the pitcher to throw, out of 100 pitches (lowest and highest round to the nearest whole number) using the 2-standard deviations rule. A value is unusually high or unusually low if it is more than >) two standard deviations away from the mean.

Answer 1

Solution :- xn Binomial M=100 p=0.7 A) F(x) = mp = 100 x 0.75 = 75 | 75 25 B) P(x=75) = (%) p* q n-> ( 109 )(675) (0.25) = 0.0918 9 Standard deviation = rmpq = V100X0.75% 0.25 4.33 d) legual range, between 1-20 and litar = 75- 2x 4.33 and 75+ 2x 4.33 = 1667 and 84 1