Question

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 9 children are chosen, the probability that exactly 4 would draw the nickel too small is:    

c) If 9 children are chosen at random, the probability that at least one would draw the nickel too small is:     

d) If 80 children are chosen at random, it would be unusual if more than    drew the nickel too small

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	21	19	40
High Income	26	9	35
Total	47	28	75

Answer 1

a) Proportion of all children that drew the nickel too small = 47/75

= 0.627

b) Binomial distribution: P(X) = nCx p^x q^n-x

Here, n = 9

p = 0.627

q = 1-p

P(exactly 4 would draw the nickel too small) = 9C4 x 0.627⁴ x (1-0.627)⁵

= 0.141

c) P(at least one would draw the nickel too small) = 1 - P(none will draw the nickel too small)

= 1 - (1-0.627)⁹

= 0.9999

d) If 80 students are chosen, mean number of students who will draw a nickel too small = np

= 80x0.627

= 50.16

Standard deviation =

= 4.325

It is considered unusual if the number is more than 2 standard deviations above mean

50.16 + 2x4.325

= 58.81

It would be unusual if more than 58 drew the nickel too small