Question

Homework: HW 4 Save Score: 0 of 1 pt 12 of 30 (11 complete) HW Score: 33.33%, 10 of 30 pts cess 5.2.15-T Question Help 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 284 <x<294 269 6 = 11 The probability that the member selected at random is from the shaded area of the graph is (Round to four decimal places as needed.)

Answer 1

Here, μ = 269, σ = 11, x1 = 284 and x2 = 294. We need to compute P(284<= X <= 294). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (284 - 269)/11 = 1.36
z2 = (294 - 269)/11 = 2.27

Therefore, we get
P(284 <= X <= 294) = P((294 - 269)/11) <= z <= (294 - 269)/11)
= P(1.36 <= z <= 2.27) = P(z <= 2.27) - P(z <= 1.36)
= 0.9884 - 0.9131
= 0.0753