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Help needed with explanations asap please!

Previous Problem Problem List Next Problem (1 point) A customs age ors 22 identically looking packets of white power in a traveler's sutcase. Unknown to the customs officer, 16 of these packets contain cocaine, the rest do not The customs officer is to randomly pick 4 packets and test each one. A random variable X is to count the number of tested packets that test positive for (a) Finish the probability distribution of X below Usa four decimals in each of your entries P(X = z) IE (b) From the distribution you found in part (a), what can you say about the distribution of X? The distribution of X is ? (c) How many of the 4 packets do you expect be to test positive for cocaine? Provide the standard deviation as well. E(X)- SD(X) (use two decimals ili (use two decimals) Preview My Answers Submit Answers

Explanation / Answer

(a) Probability of a bag containing cocaine = 16/22

P(X = 0) = (6/22)4 = 0.0055

P(X = 1) = 4 * (16/22) * (6/22)3 = 0.0590

P(X = 2) = 6 * (16/22)2 * (6/22)2 = 0.2360

P(X = 3) = 4 * (16/22)3 * (6/22) = 0.4196

P(X = 4) = (16/22)4 = 0.2798

(b) The distribution of X is binomial.

(c) E(X) = 0*0.0055 + 1*0.0590 + 2*0.2360 + 3*0.4196 + 4*0.2798

= 2.909 = 2.9.

Variance V(X) = 0*0.0055 + 1*0.0590 + 4*0.2360 + 9*0.4196 + 16*0.2798 - 2.909*2.909 = 0.793919.

SD(X) = 0.793919 = 0.89.

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