The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into thefollowing table:Too SmallToo LargeTotalLow Income211940High Income269.35Total472875Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 3 decimalplaces. 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 ofchildren), and that the remainder of the questions in this section apply to selections from thepopulation 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 toosmall is:d) If 120 children are chosen at random, it would be unusual if more thandrew the nickel too smallQuestion Help: Message instructor D Post to forumI Calculator

Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to our policy we have solved the first three sub parts. If you need help with other sub part, please re post it.a) The total number of children is 75. The total number of children that drew the nickel too small is 47. Hence, the proportion of all children that drew the nickel too small is 47/75 ≈ 0.627. b) Here, n is total number of trials and p is the success probability. Define a random variable X, which defines the number of children that drew the nickel too small. Here, n = the number of all randomly selected children that drew the nickel too small. There are total n = 5 children are selected. Consider “children that drew the nickel too small”, as success. It is obtained that 0.627 proportion of all children that drew the nickel too small. Hence, the success probability is p = 0.627. In this case, there are two outcomes, that is, whether the children that drew the nickel too small or not. These two events are independent to each other, and the probabilities of success are constant for each trial. Thus, X follows Binomial distribution with number of trials n = 5 and success probability p = 0.627. The probability that exactly 3 would draw the nickel too small is, Or, using the excel formula, =BINOM.DIST(3,5,0.627,FALSE), it can also be obtained that, P(X = 3) = 0.3429. Thus, the probability that exactly 3 would draw the nickel too small is 0.3429. c) The probability that at least one would draw the nickel too small is, Or, using the excel formula, =1-BINOM.DIST(0,5,0.627,FALSE), it can also be obtained that, P(X ≥ 1) = 0.9928. Thus, the probability that at least one would draw the nickel too small is 0.9928.