Question

16. + -18 points DevoreStat9 3.E.048. My Notes Ask Your Teacher NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children and let X be the number in the sample who have a food allergy. Then X - Bin(25, 0.05). (Round your probabilities to three decimal places.) mais des contre cele de tornare in the under the server con los (a) Determine both P(X < 4) and P(X < 4). P(X < 4) = | P(X < 4) = (b) Determine P(x > 5). P(X > 5) = (c) Determine P(1 < X < 4). P(1 < X < 4) = (d) What are E(X) and Oy? (Round your answers to two decimal places.) E(X) = (e) In a sample of 90 children, what is the probability that none has a food allergy? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Talk to a Tutor Show My Work (Required) What steps or reasoning did you use? Your work counts towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display

Answer 1

Pof of Binomial disth is meae p* (1-P) D-x x=0,1.. I DP ( X54) = P(x =o) + P(x=1) +PCX = 2) + P (x =3)+PCX = 4). = 25C (0.05 (0.95) 25; 25. co.es' co.g5) 24+25 C, (0.05) ²60.95 + 250g (0.05)3 (0.9522 + 25c4(0.05) 4 (0.9521 = 0.2774 +0.3650+ 0.2305to. 0930+ 0.0269 IP (8 (54)=0.9928 0.993 1)a P(x <4) = P(x=0) + P(x=1) + P(x=2) + P(x=3) = 0.2774 +0,3650 to 2305+0.0930 P(X24) = 0.9659 6) P(x>,5) = 1-PCX 25) = 1 [P(x=0) + P(x=1) +P (x=2) + P(x=3)+ P(x=4) = 1-[6.992.8] P(x2,5) = 0.0072), e) PCIS X 54)=P(x=1) + P(x =2) + P (8=3) + P (X= 4) 0.365 +0.2305 +0.0930 +0.0269 (18x24 50.715 d) E(x) = np = 25%0.05 E(X)=1.25) L 6x = √npg = √25x0.05x0.gs Tox= 1.0897 es prob that none has food allergy is p(x=0) PCX=0) - 90C. (0.05)° 0.95090 P (x=0) = 0.0099 a) brs:8,0.25) P (x =5) = 8cs (o.as) (0.75 -0.023) /P(x=5)=0.023 16) § 6 (6 ; 8 ,0.6) P(x=6) = 8 cc (0.6) (0.47² IP(x=6) = 0.209 c) P( 35x45) when no=7&p=0.65 = P(x=3 ) + P(x=4) + P (x =5) = ? C3 (0.65) 3 (0,354 +7C4 (0,65" (0.357 7 ? Cs (0.65) (0.35)? = 0.1442 +0.26 79 +0.28 2985 P(35X55) = 0.7106 d) P(19.5x) = P (2, 1) = 1-P (x4<1) = 1-P(x=0) =1-9co (0.15° (0.859 PC1sx) = 0.7684)