Question

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	17	23	40
High Income	23	12	35
Total	40	35	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 8 children are chosen, the probability that exactly 3 would draw the nickel too small is:     

c) If 8 children are chosen at random, the probability that at least one would draw the nickel too small is:    

Answer 1

a)

The children that drew the nickel too small (x)= 40

Total student (N) = 75

Proportion of all children that drew the nickel too small = x/N = 40/75 = 0.5333

b)  The probability that exactly 3 children draw the nickel too small out of  8 children.

This is a binomial problem,

P(X=3) = ⁸C₃ * (0.5333)³ * (1 - 0.5333)^8-3

= 56 * 0.1517*0.0221

= 0.1877

c) The probability that at least one child draw the nickel too small out of  8 children.

= 0.9977