in a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation is 5.5…

Answer:

A. 279 days

Explanation:

Step1: Find the z - score

Looking up the 18th percentile in the z - table, the z - score $z\approx - 0.92$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 284$ (mean), $\sigma = 5.5$ (standard deviation), and we want to find $x$. Rearranging for $x$ gives $x=\mu+z\sigma$.

Step3: Calculate $x$

Substitute $\mu = 284$, $z=-0.92$, and $\sigma = 5.5$ into the formula: $x = 284+( - 0.92)\times5.5=284 - 5.06=278.94\approx279$.