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 282 < x < 292 μ = 270 σ = 10 243 282 292 pregnancy length (in days) 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: Standardize the bounds

We use the z - score formula $z=\frac{x - \mu}{\sigma}$. For $x = 282$, $z_1=\frac{282 - 270}{10}=\frac{12}{10}=1.2$. For $x = 292$, $z_2=\frac{292 - 270}{10}=\frac{22}{10}=2.2$.

Step2: Find the probabilities

We know that $P(282

Step3: Calculate the probability of the interval

$P(1.2 < Z < 2.2)=P(Z < 2.2)-P(Z < 1.2)=0.9861 - 0.8849 = 0.1012$.

Answer:

$0.1012$