Question

Pregnancy Length in a Population of New Mothers 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. 283 <x<293 269 a 11 293 283 239 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.) ts no ess Enter your answer in the answer box. ? ess ibrary O 89 e here to search ASUS ZenBook

Answer 1

Here, μ = 269, σ = 11, x1 = 283 and x2 = 293. We need to compute P(283<= X <= 293). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (283 - 269)/11 = 1.27
z2 = (293 - 269)/11 = 2.18

Therefore, we get
P(283 <= X <= 293) = P((293 - 269)/11) <= z <= (293 - 269)/11)
= P(1.27 <= z <= 2.18) = P(z <= 2.18) - P(z <= 1.27)
= 0.9854 - 0.898
= 0.0874