Question

Consider the following natality statistics for the U.S. population in 1992. According to these data, the probabilities that a randomly selected woman who gave birth in 1992 was in each of the following age groups are as follows:

Age (years) Probability

< 15 0.003

15 – 19 0.124

20 – 24 0.263

25 – 29 0.290

30 – 34 0.220

35 – 39 0.085

40 – 44 0.014

45 – 49 0.001

1. What is the probability that a woman giving birth in 1992 was 40 or older? Which answer is correct? There might be slight rounding differences. Please provide an explanation.

a.	0.00015
b.		0.015
c.		0.15
d.		0.0015

2. Given that the mother of a particular child was under 30 years of age, what is the probability that she was not yet 20 years of age? Which answer is correct? There might be slight rounding differences. Please provide an explanation.

a. 0.650

b. 0.149

c. 0.205

d. 0.187

3. Given that the mother was 35 years of age or older, what is the probability that she was under 40 years of age? Which answer is correct? There might be slight rounding differences. Please provide an explanation.

a. 0.500

b. 0.107

c. 1.234

d. 0.850

Answer 1

Solution:

Given:

Age(Years)	Probability
< 15	0.003
15–19	0.124
20–24	0.263
25–29	0.290
30–34	0.220
35–39	0.085
40–44	0.014
45–49	0.001

Part 1) What is the probability that a woman giving birth in 1992 was 40 or older?

P( Age is 40 or older) =..................?

P( Age is 40 or older) = P( 40 or more)

P( Age is 40 or older) = P( 40-44 ) + P( 45-49)

P( Age is 40 or older) = 0.014 +0.001

P( Age is 40 or older) = 0.015

Thus correct answer is:

b. 0.015

Part 2) Given that the mother of a particular child was under 30 years of age, what is the probability that she was not yet 20 years of age?

P( mother  was not yet 20 years of age | she was under 30 years of age ) =.................?

that is find:

P( Less than 20 | Less than 30 ) = ..............?

P( Less than 20 | Less than 30 ) = P( Less than 20 and Less than 30 ) / P( Less than 30 )

P( Less than 20 | Less than 30 ) = P( Less than 20 ) / P( Less than 30 )

P( Less than 20 | Less than 30 ) = [ P( < 15 ) + P( 15 -19) ] / P( < 15 ) + P( 15 -19) + P( 20-24) + P( 25-29) ]

P( Less than 20 | Less than 30 ) = [ 0.003 +0.124 ] / [ 0.003 +0.124 + 0.263 + 0.290 ]

P( Less than 20 | Less than 30 ) = 0.127 / 0.680

P( Less than 20 | Less than 30 ) = 0.1867647

P( Less than 20 | Less than 30 ) = 0.187

Thus correct answer is:

d. 0.187

Part 3) Given that the mother was 35 years of age or older, what is the probability that she was under 40 years of age?

That is find:

P( Mother was under 40 years of age | she was 35 years of age or older ) =..............?

that is:

P( Less than 40 | 35 or more ) = ...............?

P( Less than 40 | 35 or more ) = P( Less than 40 and 35 or more ) / P( 35 or more )

P( Less than 40 | 35 or more ) = P( 35 - 39 ) / [ P( 35 - 39 ) + P(40-44) + P( 45-49) ]

P( Less than 40 | 35 or more ) = 0.085 / [ 0.085 + 0.014 + 0.001 ]

P( Less than 40 | 35 or more ) = 0.085 / 0.100

P( Less than 40 | 35 or more ) = 0.850

Thus correct answer is:

d. 0.850