Question

NAME MATH 164, $6.2 WORKSHEET SPRING 2020 PERRY ALIADO Calculate the mean, standard deviation, and probability for the following binomial experiments with the following numerical properties. You may need to use an additional blank sheet of paper to fit in your probability calculations. Activity: shooting free throws Number of free shows attempted = 8 free throws Probability of successfully making a free throw = 83.6% (Hint: what is this as a decimal?) Number of successful free throws we want = 7 throws Activity: picking dominoes (using a "Double-Six" domino set) Number of times we pick a domino, then put it back into the pile = 6 times Probability of successfully picking a "doubles" domino = 7/28 (Hint: what is this as a decimal?) Number of times we want to pick a "double" domino = 2 times 3) Activity: getting divorced Number of married couples we are studying = 9 married couples Probability of the couple getting divorced = 47.2% (Hint: what is this as a decimal?) Number of divorces we want to see = 5 divorces
please answer all 3 circled questions

Answer 1

7 Calculate mean standard deviation, and albe probability for the following benomial experiments with the following numerical Properties. You may need to use an additional blank sheet of paper to fit in your probability calculations. 0 Aduity shooting free threws free & Number of shows attempted free throws' Probability of successful making a free throw = 8.6 % Number of successfeel free throws we count = of throws. Let p be the probability of successful making a free throw = 83.6% = 83.6 = 0.8 36 100 6. P ( success) = 0.836 - P and PC Failure ) = L - P (success) = 1-0.836 P(A) = 0.164 = 9 80, P(S) = 0.836 and PCR)=0.164 Number of free throws (n = 8 As eve know the mean of Binomial distributh mean = np = 8x0.836 mean = 6.688

and the raciance of Binomial distribution is Variance = npq. = 8* 0.836 x 0.164 variance = 1.097 and standard deviation is root square of nariance . 8.D Tran PE=V1.097 15.0 = 1,048 Probability for The Binomial distribution, P (x=x) = (2) p?.qp2 ; x = 0,1,2 --.8 P68=7) = 8, 10.98694.co.1648-7 = 8! x 0.29 X 0.164 (8-7)!7! 8x7 x 0.048 17 = = 8x0.048 = 0.38048 O Ta o p (x=7) = 0.38

Achinity: Picking domi onnity: Picking dominoee luging 'Double sin' domino set Number of times coe pick a domino, then put it a back into the piele = 6 times Probability of successfully picking a doubles domino = 728 Number of times we coant to pick double domino = 2 times het p be the probability of successfully pa a double domino = 7/28 = 0.25 Therefore, P = 0.25 and q=1-p = 0.75 Number of times we pick a domino = 6 times n = 6 80, the mean of Binomial dismi butión ice, I= np = 6x0.25 Til = 1.5 and the variance of Binomial distribution is, o2 = npq = 6x0.25 x 0.75 O2 = 1.125 o=1.06 o 18.D. = 1.061 probability for the Binomial distibution is, PC&=x) = nc;p?q?, 4X=1,2...n PLX=2) = 6C, (0.253² (0-4576-2

= 6! 0.0625 X 10.5)4 (6-2)!2! 2 = 96-45x400625 x 0. OLDAL E4 X2X1 wurde ind = 15 x 0.0625 %0.316de = 0.29625 1 PCx=2] = 0.30 in ☺ Activity: yetting divorced Number of married couples we are studying = 9 maried couples" probability of Ilhe couple getting divorced = 47.2% Number of divorces we want to see = 5 diroces het p be the probability of the couple getting divorced = 44.2% = 47.2 . P = 0.472 Therefore, q = 1-P = 1-0.472 = 0.528 Numbe of mamed couples eve are studying = 9 married couples le On = 9 30, mean = np = 9x0.472 = 4.248 i fill = 4.248

and variance = npq 02= 9x0.472 X 0.528 72 - 2.942944 DE 12.242944 = 7:49764615 :18.0.21.50 Probability for the Binomial dig hibution is, P[x = x3 = nex peg nox x x = 1,2...n P (x = 6.]=9c560.47239 6052899-5, x=192-98 = 9*0.023 % (0.52809 (9-5)!5! = 9x8x7x6x5? *0.023 x 0.08 4155 3x8 x 7 x 6 x 0.001 Ихххх = 0.926 o P[x=5] = 0.1261