48E

Answer: Step 1 of 3 Given that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children. Let X be the number in the sample who have a food allergy. Then X ~ B(25, 0.05) a. We need to determine P(X 3) and P(X < 3) P(X 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) Using Excel function, “=BINOMDIST(x,n,p,false)” x P(x) 0 0.277389573 1 0.36498628 2 0.230517651 3 0.093015894 Sum 0.965909399 Therefore, P(X 3) = 0.9659. Now, P(X < 3) x P(x) 0 0.277389573 1 0.36498628 2 0.230517651 Sum 0.872894 Therefore, P(X < 3) = 0.8728 Step 2 of 3 b. Here, we need to determine P(X 4) Using Excel function, “=BINOMDIST(x,n,p,false)” x P(x) 4 0.026925654 5 0.005951987 6 0.001044208 7 0.000149173 8 0.0000176 9 0.00000175 10 0.000000147 11 0.0000000106 12 0.000000000651 13 0.0000000000343 14 1.54747E-12 15 5.97268E-14 16 1.9647E-15 17 5.47439E-17 18 1.28056E-18 19 2.48308E-20 20 3.92065E-22 21 4.91309E-24 22 4.70152E-26 23 3.22759E-28 24 1.41561E-30 25 2.98023E-33 Sum 0.034090601 Therefore, P(X 4) = 0.0341 Alternate method: P(X 4)= P(X 25) P(X 3) [P(X 25)= 1 since sum of all probabilities must be 1] = 1 - 0.9659 = 0.0341