the total number of forks dropped by customers per day at a busy restaurant is multimodal with a mean of…

Explanation:

Step1: Identify the formula for z - score

The formula for the z - score of a sample mean 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: Substitute the given values

We are given that $\mu = 24.5$, $\sigma=3.3$, $n = 80$, and $\bar{x}=25$. $z=\frac{25 - 24.5}{\frac{3.3}{\sqrt{80}}}$ First, calculate $\sqrt{80}\approx8.944$. Then $\frac{3.3}{\sqrt{80}}\approx\frac{3.3}{8.944}\approx0.37$. $z=\frac{25 - 24.5}{0.37}=\frac{0.5}{0.37}\approx1.35$.

Step3: Find the probability

We want to find $P(\bar{X}>25)$, which is equivalent to $P(Z > 1.35)$ using the standard normal distribution. Since $P(Z>z)=1 - P(Z\leq z)$, and from the standard - normal table $P(Z\leq1.35) = 0.9115$. So $P(Z > 1.35)=1 - 0.9115=0.0885\approx0.088$.

Answer:

0.088