Question

In one city, 20% of the population has a college education. Three people are selected at random from the city. Find the probability distribution of X, the number among the three that have a college education. A. Identify then and the p for this distribution. p B. Let the random variable x be the possible number of people selected with a college degree. Develop a binomial distribution by finding P(x) when x = 0, 1, 2, and 3. XP(x) 0 1 2.

Answer 1

Given = ) education neo P(X) = 360.2° (0.8) 3-0 P(X=2)=34 201. of population has education P-0.2 (Probability for having) 3 people are seleded randomly =) n = 3 The give problem follow binomial distribution. P(x) p> { r-ph-y -) n=3 Q(x - 1) 3 + 2) ( 8)”. At X=3 P(X=3)=3 835 (0-2)3 = 0.008 P=0.2 B 0.512 Atx=0 0.384. At X=1 Atx=2 -33

P (X) 0.512 O - 0.384. ooo96 2 008 3 © prccal least 1) - PCX=1) +PCX = 2) + P(x = 3) PCX=0) + P(X=1) + P(X= 2) + P (X=3) = 1 L Probability rule =) P (X=1) + P(X= 2) + P(X=3) alap(x=0) Therefore Prcat least 1) Prralleust 1) - 1 - P(X=0) 10.512. = 0.488 Pr Callecast 4) = 0.488)

= ncp) [ formula for mean Binomial distribult) in mean = 3(0.2) = 0.6 expected no: = 0.6. 82 Valianco n (P) (1-P) (formula for variance) 3(0.2) (0.8) 360.16) = 0.48 = z a 0.4.8 = 50.48 = 0.692. Standal deviation of = 0.692