Question

1. mrs. gs first daughter was 4.85 kg when she was born. the weights of newborn baby girls follow a normal distribution with a mean of 3.54 kg and a standard deviation of 2.43 kg. mrs. g knows that she will be having a son for her second child. newborn males follow a normal distribution with a mean of 3.78 kg and a standard deviation of 2.96 kg. what does her newborn baby boy have to weigh, to match her newborn baby girls z - score? (a) 1.07 kg (b) 4.61 kg (c) 4.89 kg (d) 5.09 kg (e) 5.38 kg

Explanation:

Step1: Calculate the z - score of the baby girl

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. For the baby girl, $x = 4.85$ kg, $\mu=3.54$ kg and $\sigma = 2.43$ kg.
$z_{girl}=\frac{4.85 - 3.54}{2.43}=\frac{1.31}{2.43}\approx0.54$

Step2: Set up the equation for the baby boy's weight

Let the weight of the baby boy be $x$. For baby boys, $\mu = 3.78$ kg and $\sigma=2.96$ kg. We want $z_{boy}=z_{girl}$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$, we substitute $z = 0.54$, $\mu = 3.78$ and $\sigma = 2.96$ and solve for $x$.
$0.54=\frac{x - 3.78}{2.96}$

Step3: Solve the equation for $x$

Multiply both sides of the equation by $2.96$: $0.54\times2.96=x - 3.78$.
$1.60 = x-3.78$.
Add $3.78$ to both sides: $x=1.60 + 3.78=5.38$ kg

Answer:

E. 5.38 kg