The correct size of a nickel is 21.21 millimeters. Based on that, the data can b

Question

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table: Too Smal Too Large Total 40 35 35 75 15 25 40 25 10 Low Income High Income Total 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: Preview 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 6 children are chosen, the probability that exactly'3 would draw the nickel too small is: Preview c) If 6 children are chosen at random, the probability that at least one would draw the nickel too small is: Prevjew d) If 120 children are chosen at random, it would be unusual if more than Preview drew the nickel too small

Explanation / Answer

a)
P(too small) = 40/75

b)
X = number of children who draw the nickel too small
X follow binomial with n = 6 , p = 0.53333333333
P(X = 3) = 6C3 *p^3 * q^3
= 20 * 0.53333333333^3 *(1 -0.53333333333)^3
= 0.30835182441

c)
P(X<=1) = 1- P(X = 0)
= 1 - (1-p)^n
= 1- (1-0.533333)^6
= 0.98967137411

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