Question

1. mrs. gs newborn baby girl sleeps for approximately 20.1 hours per day. newborn sleep schedules are normally distributed with a standard deviation of 0.8 hours. if you know mrs. gs daughter has a sleep z - score of 0.4375, what is the mean sleep time of all baby girls? (a) 19.75 hours (b) 19.98 hours (c) 20.35 hours (d) 18.45 hours (e) 21.45 hours

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $z$ is the z - score, $x$ is the observed value, $\mu$ is the mean, and $\sigma$ is the standard deviation. We are given that $x = 20.1$ hours, $z=0.4375$, and $\sigma = 0.8$ hours, and we need to solve for $\mu$.

Step2: Rearrange the z - score formula

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$ to get $z\sigma=x - \mu$. Then, we can rewrite it as $\mu=x - z\sigma$.

Step3: Substitute the given values

Substitute $x = 20.1$, $z = 0.4375$, and $\sigma=0.8$ into the formula $\mu=x - z\sigma$. So, $\mu=20.1-0.4375\times0.8$.
First, calculate $0.4375\times0.8 = 0.35$. Then, $\mu=20.1 - 0.35=19.75$.

Answer:

A. 19.75 hours