a newborn who weighs 2,500 g or less has a low birth weight. use the information on the right to find the z…

a newborn who weighs 2,500 g or less has a low birth weight. use the information on the right to find the z - score of a 2,500 g baby. what is the z - score of a newborn who weighs 4,000 g? what weight would give a newborn a z - score of - 0.75? grams 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. $z=\frac{x - mu}{sigma}$

a newborn who weighs 2,500 g or less has a low birth weight. use the information on the right to find the z - score of a 2,500 g baby. what is the z - score of a newborn who weighs 4,000 g? what weight would give a newborn a z - score of - 0.75? grams 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. $z=\frac{x - mu}{sigma}$

Answer

Explanation:

Step1: Recall z - score formula

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. We are given $\mu = 3500$, $\sigma=500$ and $z=- 0.75$, and we need to find $x$.

Step2: Rearrange the formula to solve for $x$

Starting from $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x - \mu$. Then add $\mu$ to both sides to get $x=\mu+z\sigma$.

Step3: Substitute the given values

Substitute $\mu = 3500$, $z=-0.75$ and $\sigma = 500$ into the formula $x=\mu+z\sigma$. So $x=3500+( - 0.75)\times500$. First, calculate $( - 0.75)\times500=-375$. Then $x=3500 - 375$. $x = 3125$.

Answer:

3125