The correct size of a nickel is 21.21 millimeters. Based on that, the data can b
ID: 3255462 • Letter: T
Question
The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table: 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) 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 5 children are chosen, the probability that exactly 3 would draw the nickel too small is: c) If 5 children are chosen at random, the probability that at least one would draw the nickel too small is: d) If 120 children are chosen at random, it would be unusual if more than drew the nickel too smallExplanation / Answer
(a) Part a is correct as you have done it correct.
(b) If 5 Children are chosen, probability that exactly 3 would draw the nickel too small is =?
we first calculater the probability of nickel too small = 44/75 = 0.5867
so Pr ( exactly 3 would draw the nickel too small) = 5C3 (0.5867)3 (0.4133)2 = 0.345
(c) Probability that at least one would draw the nickel too small is
Pr ( at least one would draw nickel too small) = 1 - Pr ( Noone would draw nickel too small)
= 1 - 5C0 ( 0.5867)0 (0.4133)5 = 0.988
(d) If 120 children are chosen at random
so Mean number of persons would draw nickel too small x= 120 * 44/75 = 70.4
Standard deviation of persons would draw nickel too small (s) = sqrt [120 * (44/75) * (1 - 44/75) ] = 5.3943
so It would be unusual if it would be more than x + 2s = 70.4 + 2 * 5.3943 = 81.18
so if number of children are more than 81.18, it would be unusual.
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