Question

assume a member is selected at random from the population represented by the graph. find the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed. the probability that the member selected at random is from the shaded area of the graph is (round to four decimal places as needed.)

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu = 268$ and $\sigma=19$.
For $x = 284$, $z_1=\frac{284 - 268}{19}=\frac{16}{19}\approx0.84$.
For $x = 291$, $z_2=\frac{291 - 268}{19}=\frac{23}{19}\approx1.21$.

Step2: Find probabilities from z - table

We use the standard normal distribution table.
$P(0.84From the z - table, $P(Z < 1.21)=0.8869$ and $P(Z < 0.84)=0.7995$.

Step3: Calculate the final probability

$P(0.84

Answer:

$0.0874$