the cost to produce a batch of granola bars is approximately normally distributed with a mean of $7.19 and a…

Explanation:

Step1: Calculate the standard error

The formula for the standard error of the mean is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma = 0.86$ is the population standard - deviation and $n = 12$ is the sample size. $\sigma_{\bar{x}}=\frac{0.86}{\sqrt{12}}\approx\frac{0.86}{3.4641}\approx0.2483$

Step2: Calculate the z - score

The formula for the z - score is $z=\frac{\bar{x}-\mu}{\sigma_{\bar{x}}}$, where $\bar{x}=7.00$, $\mu = 7.19$ and $\sigma_{\bar{x}}\approx0.2483$. $z=\frac{7.00 - 7.19}{0.2483}=\frac{- 0.19}{0.2483}\approx - 0.765$

Step3: Find the probability

We want $P(\bar{X}>7.00)$, which is equivalent to $P(Z>-0.765)$. Since $P(Z > z)=1 - P(Z\leq z)$, and from the standard normal table $P(Z\leq - 0.765)\approx0.2220$. So $P(Z>-0.765)=1 - 0.2220 = 0.7780$

Answer:

0.7780