Question

Suppose that you and two friends go to a restaurant which last month filled approximately 89.2% of the orders correctly.

a. What is the probability that all three orders will be filled correctly?
b. What is the probability that none of the three orders will be filled correctly?
c. What is the probability that at least two of the three orders will be filled correctly?
d. What are the mean and standard deviation of the binomial distribution used in a through d

Probability of Correct Order at Restaurant B Data Sample size Probability of an event of Interest P. - Hs Mean Variance Standard Deviation 0.36.14 0.6026 Binomial Probabilities Table X PX PISX) PL<XP/>X) PEX) 0 0.0028 0.0028 0.0000 0.9971 0.9990 1 0.0512 0.0540 0.0028 0.9459 09971 20.3121 03661 00540 0.6338 09459 3 0.6338 0.9999 0.3661 0.0000 0.6338 Probability of Correct Order at Restaurant C Data Sample size Probability of an event of interest 917 Parameters Wenn Variance Standard Deviation Binomial Probabilities Table 2.751 02283 04778 X PIX) PSX) P<X) PY>X) Plex) 0.0006 0.0006 0 0000 0.9995 10001 1 0.0190 0.0196 0.0006 0.9905 0.9995 2 02094 0 2290 0.0198 0.77110.9805 3 0.7711 1.0001 0 2290 0.0000 0.7711

Answer 1

Solabon: M3 bo.892 X Bimomial Pla) ()"7 3 0 la) Plx 3) ( 0.892)1-0892) 0.097 3 (.892 (0 . 108) (b) Plx:0) 0.00 13 Plx32) P(x-2) +P3) 3-3 3 3-2 2 0.892) (0.1ol) )o.89) (01 e3) 2 0.9675 (el) Mean - 3 x .89 2 2.676 S.de 17 0.538