Question

According to the National Center for Health Statistics (2018), there were 3,855,500 births registered in the United States in the year 2017. The mean age of mothers at first birth was 26.8 years. Lets suppose that the standard deviation is 3 years. Use this information to answer questions #1 through #4.

Question 1

What proportion of first time mothers gave birth before the age of 18?

Question 2

What proportion of first time mothers gave birth after the age of 25

Question 3

What proportion of first time mothers gave birth between the ages of 20 and 30?

Question 4

What proportion of first time mothers gave birth after the age of 35?

Answer 1

Since the births are about 3855500 which is very large we can model it using normal distribution. therefore

z-score = = (x- 26.8) / 3

then using the normal dsitribution tables we can calculte the probabilties. Prbabilties can be multiplied by 100 to get them in pecentage form. If we want to get the number then we can multiply the probabilities ti 3855500

Question 1

What proportion of first time mothers gave birth before the age of 18?

P( X < 18) = P( Z < -2.93)

=1 - P(Z <2.93)

= 1 - 0.9983

P( X < 18) =

Question 2

What proportion of first time mothers gave birth after the age of 25

P(X > 25) = P( Z > -0.6)

= P( Z < 0.6)

P( X > 25) =

Question 3

What proportion of first time mothers gave birth between the ages of 20 and 30?

P(20 <X < 30) = P( X < 30) - P( X < 20)

= P( Z < 1.07)- P( Z < -2.27)

= P(Z< 1.07) - [ 1 - P(Z < 2.27) ]

= 0.8539 - (1 - 0.9883)

P( 20 < X < 30) =

Question 4

What proportion of first time mothers gave birth after the age of 35?

P( X > 35) = P( Z > 2.73)

= 1 - P( Z > 2.73)

= 1 - 0.9969

P(X > 35) = 0.00314

Q	P	%	No.
1	0.001677	0.17%	6464.587
2	0.725747	72.57%	2798117
3	0.845234	84.52%	3258798
4	0.003135	0.31%	12086.38