Question

The correct size of a nickel is 21.21 millimeters. Children of low- and high-income households were asked to draw a nickel of actual size. Based on that, the data can be summarized into the following table: Too Small Total Too Large 19 Low Income 21 40 21 14 35 High Income Total 42 33 75 Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 4 decimal places. Give your answer to part d as a whole number.) a) The proportion of all children that drew the nickel too small is: Assume that this proportion is true for ALL children (e.g. that this proportion applies to any group of children), and that the remainder of the questions in this section apply to selections from the population of ALL children. b) If 9 children are chosen, the probability that exactly 3 would draw the nickel too small is: c) If 9 children are chosen at random, the probability that at least one would draw the nickel too small is: d) If 90 children are chosen at random, it would be unusual if or more drew the nickel too small. (Assume unusual is more than 2 SD from the mean.) Submit Question

Answer 1

sol Given Table, Too Small Too large Tola low income 21 40 High income 21 14 35 Tolal 42 33 75. a) The proportion of all children that drew the nickel too small 42 = 0.56 75 let X be random Variable denoten The number of children who draw the nickel too small out of 9. n = 9 P = 0.56 X~ Binomiall n=9, p=0.56) The probabilly man function of xin 9-X P(x=x)= (a) (0.55 (1-0.56) 2012... a Here, need to find P(x=3) 9-3 (0.56) (0.44) P(X=3) 3 10.56) (19) (0.563"conto

= (84) (0.175616) (0.00725631385) 0-10 704328438 ł 0.1070 c) Here, we need to find P(x) P(X),1)= 1- P(XL1) = P ( X =o) -[(:) (0.51% contro] - - 0.0006182183 = 0.99938187816 0.9994 d2 Here, n=90 Since this follows Binomial distribution, Mear, p= np= (90) (0.56)= 50.4 Sländard deviation, o=Supli-p) (90) (0.56 (1-0.56) =4.70914004 888 a 4. 709) We consider away unusual if it lien 2 so from the mean. H + 20 = 50.4 + 2* 4.7091 59.8182 ~ 60 It go Children are choren unusual it at random, it would be the nickel too small. 60 drew more