Question

the weight of newborn babies has a normal distribution with mean 7.5 pounds and standard deviation 1.75 pounds. a baby born 280 weeks early has a standard score of -1.5. what is the baby’s actual weight? round your answer to the nearest hundredth. the baby weighed \boxed{} pounds at birth.

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $z$ is the standardized score, $x$ is the raw score, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

Step2: Rearrange to solve for $x$

Rearrange the formula to isolate $x$: $x = \mu + z\sigma$

Step3: Substitute given values

Substitute $\mu = 7.5$, $z = -1.5$, $\sigma = 1.75$:
$x = 7.5 + (-1.5)(1.75)$

Step4: Calculate the result

First compute $(-1.5)(1.75) = -2.625$, then add to 7.5:
$x = 7.5 - 2.625 = 4.875$
Round to the nearest hundredth: $x = 4.88$

Answer:

4.88