1 A certain town has 30000 families The average number of ch

1. A certain town has 30,000 families. The average number of children per family is 2.4 with an SD of 0.9. Also, 20% of the families have no children at all. A random sample of 100 families from that town is drawn. PART I: a) Find the expected value and the standard error for the percentage of families chosen without children? b) Estimate the chance that somewhere between 25% and 30% of the sample families will have no children? PART II: a) Find the expected value and the standard error for the average number of children per family in the sample b) Estimate the chance that the average number of kids per family in the sample is greater than 2.5

Solution

1) a. Expected value = 20

std error = 20(0.8)/rt 100 = 1.6

b) Prob (25<x<30%) = P(5/1.6 <z<10/1.6)

= P(3.125<z<6.259) = 0.00

Part II:

Expected no of children = 240

P(X>2,5) = P(Z>0.1/0.09) = P(Z>1.11) = 0.1335