Question

madison is studying flocks of birds in her state. the mean number of birds in a flock is 16, and the standard deviation is 4. flock a is two standard deviations away from the mean. which of the following statements is true? flock a has 8 birds. flock a has 20 birds. flock a has 8 or 24 birds. flock a has 12 or 20 birds.

Explanation:

Step1: Calculate lower - bound value

The formula to find a value that is $k$ standard deviations away from the mean $\mu$ is $x=\mu - k\sigma$ (for the lower - bound when $k$ is positive). Here, $\mu = 16$, $\sigma=4$ and $k = 2$. So, $x_1=16-2\times4$.
$x_1=16 - 8=8$.

Step2: Calculate upper - bound value

The formula for the upper - bound is $x=\mu + k\sigma$. Substituting $\mu = 16$, $\sigma = 4$ and $k = 2$, we get $x_2=16+2\times4$.
$x_2=16 + 8=24$.

Answer:

C. Flock A has 8 or 24 birds.