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 area of the graph. assume the variable x is normally distributed. sat critical reading scores 200 < x < 400 μ = 511 σ = 112 click to view page 1 of the standard normal table click to view page 2 of the standard normal table. 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 $z=\frac{x-\mu}{\sigma}$.
For $x = 200$, $z_1=\frac{200 - 511}{112}=\frac{- 311}{112}\approx - 2.78$.
For $x = 400$, $z_2=\frac{400 - 511}{112}=\frac{-111}{112}\approx - 0.99$.

Step2: Use the standard - normal table

We want to find $P(-2.78From the standard - normal table, $P(Z < - 0.99)=0.1611$ and $P(Z < - 2.78)=0.0027$.
Then $P(-2.78$P(-2.78

Answer:

$0.1584$