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. pregnancy length in a population of new mothers μ = 268 σ = 10 284 < x < 291 241 284 291 pregnancy length (in days) the probability that the member selected at random is from the shaded area of the graph is 0.0874 (round to four decimal places as needed.)

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$.
For $x = 284$, $z_1=\frac{284 - 268}{10}=\frac{16}{10}=1.6$.
For $x = 291$, $z_2=\frac{291 - 268}{10}=\frac{23}{10}=2.3$.

Step2: Use the standard normal distribution table

We want to find $P(1.6We know that $P(1.6From the standard - normal distribution table, $P(Z < 2.3)=0.9893$ and $P(Z < 1.6)=0.9452$.
So, $P(1.6

Answer:

$0.0441$