destiny performs a hypothesis test on a population with $mu = 115$ and $sigma = 30$. her sample size is 25…

Explanation:

Step1: Recall z - statistic formula

The formula for the z - statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size.

Step2: Identify given values

We are given that $\mu = 115$, $\sigma=30$, $n = 25$, and $\bar{x}=120.4$.

Step3: Calculate $\frac{\sigma}{\sqrt{n}}$

First, calculate $\sqrt{n}=\sqrt{25}=5$. Then $\frac{\sigma}{\sqrt{n}}=\frac{30}{5}=6$.

Step4: Calculate the z - statistic

Substitute the values into the z - statistic formula: $z=\frac{120.4 - 115}{6}=\frac{5.4}{6}=0.90$.

Answer:

0.90