The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:
Too Small Too Large Total
Low Income 13 27 40
High Income 26 9 35
Total 39 36 75
Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 3 decimal places. Give your to part d as a whole number.)
(a) Find the proportion of all children that drew the nickel too small, for accuracy express your answer as a fraction:
Assume that this proportion is true for ALL children in an entire population (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 8 children are chosen, find the probability that exactly 6 would draw the nickel too small, round your answer to four decimals:
(c) If 8 children are chosen at random, find the probability that at least one would draw the nickel too small, round your answer to four decimals:
(d) If 100 children are chosen at random, it would be unusual if more than
drew the nickel too small, express your answer as a whole number.
(a) last line of the table ... 1st column / 3rd column
(b) this a binomial distribution ... too Small or too Large
... p(S) = 39/75 ... p(L) = 36/75
... (S + L)^8 = S^8 + 8 S^7 L + 28 S^6 L^2 + ... + L^8
... the 3rd term is the solution ... 28 * (39/75)^6 * (36/75)^2
(c) also binomial
... "at least one" means NOT none ... 1 minus the last term ... 1 - (36/75)^8
(d) 100 * (39/75) = ?