17) mrs. gs newborn baby girl sleeps for approximately 20.1 hours per day. newborn sleep schedules are…
17) 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
Answer
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