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 19 21 40
High Income 22 13 35
Total 41 34 75

Q: If 100 children are chosen at random, it would be unusual if more than_______ drew the nickel too small

The expected number would be 41/75 * 100 = 55, but I don't see data that would allow me to estimate a significant difference from that value.

Here is the entire problem I am working on.

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 19 21 40
High Income 22 13 35
Total 41 34 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) 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 2 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 100 children are chosen at random, it would be unusual if more than drew the nickel too small

To find the answer, we need to calculate the probability of a child drawing the nickel too small and then determine the expected number of children who would draw it too small.

First, let's calculate the probability of a child drawing the nickel too small for each income group. We can do this by dividing the number of children who drew it too small by the total number of children in each income group.

For the low-income group:
Probability of drawing the nickel too small = Number of children who drew it too small / Total number of children in the low-income group
Probability of drawing the nickel too small = 19 / 40 = 0.475

For the high-income group:
Probability of drawing the nickel too small = Number of children who drew it too small / Total number of children in the high-income group
Probability of drawing the nickel too small = 22 / 35 ≈ 0.629

Now, let's find the expected number of children who would draw the nickel too small. We can multiply the probability of drawing the nickel too small for each income group by the total number of children in that income group, and then sum up the results.

Expected number of children from the low-income group drawing the nickel too small = Probability of drawing the nickel too small in the low-income group * Total number of children in the low-income group
Expected number of children from the low-income group drawing the nickel too small = 0.475 * 40 = 19

Expected number of children from the high-income group drawing the nickel too small = Probability of drawing the nickel too small in the high-income group * Total number of children in the high-income group
Expected number of children from the high-income group drawing the nickel too small = 0.629 * 35 ≈ 22

Next, let's find the total expected number of children who would draw the nickel too small:
Total expected number of children drawing the nickel too small = Expected number of children from the low-income group drawing the nickel too small + Expected number of children from the high-income group drawing the nickel too small
Total expected number of children drawing the nickel too small = 19 + 22 = 41

Therefore, based on the given data, it would be unusual if more than 41 children drew the nickel too small out of a random sample of 100 children.