Question

. A certain town has 25,000 families. The average number of children per family is 2.4 with an SD of 1.1 . Also, 20% of the families have no children at all. A random sample of 400 families from that town is drawn.

a) Find the expected value and the standard error for the percentage of families chosen without children?

b) Estimate the chance that somewhere between 17% and 19% of the sample families will have no children?

c) Find the expected value and the standard error for the average number of children per family in the sample

d) Estimate the chance that the average number of kids per family in the sample is greater than 2.5

Answer 1

Solution :

(a)

Expected value for the percentage of families chosen without children = 20%

Standard error for the percentage of families chosen without children = = 2%

(b)

Chance that somewhere between 17% and 19% of the sample families will have no children = P(0.17 < < 0.19)

= P{(0.17 - 0.20)/0.02 < Z < (0.19 - 0.20)/0.02}

= P(-1.5 < Z < -0.5)

= 0.2417

= 24.17%

(c)

Expected value for the average number of children per family in the sample = 2.4

Standard error for the average number of children per family in the sample = 1.1/√400 = 0.055

(d)

The chance that the average number of kids per family in the sample is greater than 2.5 = P( > 2.5)

= P{Z > (2.5 - 2.4)/0.055}

= P(Z > 1.818)

= 0.0345

= 3.45%

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