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 u=508 6 = 123 200 800 400 Score (Round to four decimal places as The probability that the member selected at random is from the shaded area of the graph is needed.) Enter your answer in the answer box.

Answer 1

Here, μ = 508, σ = 123, x1 = 200 and x2 = 400. We need to compute P(200<= X <= 400). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (200 - 508)/123 = -2.5
z2 = (400 - 508)/123 = -0.88

Therefore, we get
P(200 <= X <= 400) = P((400 - 508)/123) <= z <= (400 - 508)/123)
= P(-2.5 <= z <= -0.88) = P(z <= -0.88) - P(z <= -2.5)
= 0.1894 - 0.0062
= 0.1832