in the united states, birth weights of newborn babies are approximately normally distributed with a mean of…

in the united states, birth weights of newborn babies are approximately normally distributed with a mean of $mu = 3,500$ g and a standard deviation of $sigma = 500$ g.\nwhat percent of babies born in the united states are classified as having a low birth weight (< 2,500 g)? explain how you got your answer.

in the united states, birth weights of newborn babies are approximately normally distributed with a mean of $mu = 3,500$ g and a standard deviation of $sigma = 500$ g.\nwhat percent of babies born in the united states are classified as having a low birth weight (< 2,500 g)? explain how you got your answer.

Answer

Answer:

2.28%

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$. Here, $x = 2500$, $\mu=3500$, and $\sigma = 500$. So, $z=\frac{2500 - 3500}{500}=\frac{- 1000}{500}=-2$.

Step2: Use the standard normal distribution table

The standard - normal distribution table gives the cumulative probability $P(Z < z)$. Looking up $z=-2$ in the standard - normal distribution table, we find that $P(Z < - 2)=0.0228$.

Step3: Convert to percentage

To convert the probability to a percentage, we multiply by 100. So, $0.0228\times100 = 2.28%$.