Answer to Question #312589 in Statistics and Probability for maggie

Question

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:

Too SmallToo LargeTotalLow Income172340High Income251035Total423375

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:    

Answer 1

a. P=42/75

b.n=5, x=2

$P(x)=nCx∗(p x )∗((1−p) (n−x) )$

$P(2)=5C2∗(p 2 )∗((1−p) (3) )= 3!2! 5! ​ ( 75 42 ​ ) 2 ( 75 33 ​ ) 3 =10x0.314x0.085=0.267$

C. $(38/75) 5 +5(38/75) 4 (37/75)+10(38/75) 3 (37/75) 2 +10(38/75) 2 (37/75) 3 +5(38/75)(37/75) 4 =0.033+0.163+0.317+0.308+0.150=0.971$