Question

A maternity says that 18% of their newborns falls in the below-weight class. 38% of these newborns are born to couples that earn minimum wage. When compared, just 14% of newborn NOT recorded as below-weight arrives to earning minimum-wage earning couples.

1. Calculate the percentage of every newborn at the maternity coming into a home with minimum-wage earning couple?
2. Compute the probability that a newborn coming to a minimum-wage earning couple would be recorded below-weight?
3. Let’s say that a randomly selected group of 4 newborn are recorded as below-weight and 5 babies were recorded NOT below-weight. What is the probability that you’ll get exactly 3 newborns from this total of 9 newborn going to minimum-wage earning couple?

Answer 1

P( Newborn Below- weight) = 0.18; P( NOT below weight) = 1-0.18 = 0.82

P( Minimum wage | Below -weight) =0.38; P( Not minimum wage | Below weight) = 1- 0.38 = 0.62

P( Minimum wage | NOT below -weight) =0.14; P( NOT minimum wage | NOT below weight) = 1-0.14 =0.86

a) P( Minimum wage)

= P( Minimum wage | Below -weight) * P( Below weight) + P( Minimum wage | NOT below -weight)*P( NOT below weight)

= 0.38 * 0.18 + 0.14 * 0.82

= 0.1832

b) P( Below weight | Minimum wage)

=

=

=0.3734

c)   P(Below weight ) = 4/9 - 0.4444

P( NOT below weight( = 5/9 = 0.5556
P( Exactly 3 newborn below -weight) = 9C3 ( 0.4444)3 ( 1-0.4444)6 = 0.2168