Question

question 5 of 10 > the lengths of footlong sub sandwiches at a local sub shop follow an approximately normal distribution with unknown mean $mu$ and standard deviation 0.2 inch. if 20% of these sandwiches are shorter than 11.7 inches, find the mean length $mu$. mean = 12.04 inches (round to 2 decimal places.) incorrect answer

Explanation:

Step1: Find the z - score

We know that if 20% of the sandwiches are shorter than 11.7 inches, we look up the z - score corresponding to a left - tail area of 0.20 in the standard normal distribution table. The z - score $z$ such that $P(Z

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 11.7$ inches is the value from the original distribution, $\mu$ is the mean of the original distribution, and $\sigma = 0.2$ inch is the standard deviation of the original distribution.
Substitute the known values into the formula: $-0.84=\frac{11.7-\mu}{0.2}$.

Step3: Solve for $\mu$

First, multiply both sides of the equation by 0.2: $-0.84\times0.2=11.7 - \mu$.
$-0.168 = 11.7-\mu$.
Then, add $\mu$ to both sides: $\mu-0.168 = 11.7$.
Finally, add 0.168 to both sides to get $\mu=11.7 + 0.168=11.87$ inches.

Answer:

$11.87$