Question

Moderate prematurity refers to babies who are born between 28 and 32 completed weeks gestational age with a birth weight range between 1500 and 2500 grams. The length of time a baby has spent in the womb, or more specifically the number of completed weeks of frequency, is called gestational age. Based on their gestational age and their weight, premature babies are placed into categories of mild, moderate and extreme prematurity. Mild Prematurity Moderate Prematurity Extreme Prematurity refers to babies who are refers to babies who are refers to babies who are between 33 and 36 born between 28 and 32 born before 28 completed completed weeks of completed weeks of weeks of gestation or a gestation and /or have a gestation with a birth birth weight less than birth weight between 1500 weight range between 1000 grams. and 2500 grams. 1000 and 1500 grams. a. Generally speaking, the gestation time for human babies is approximately normally distributed, with an average of 40 weeks and a standard deviation of two weeks. i. Calculate the probability of having a birth with mild prematurity. Explain steps and show calculation. ii. What is the probability of having a birth with extreme prematurity? Explain steps and show calculation. Iii. Find the upper and lower quartiles for the gestation times Iv. Would it be unusual to deliver a baby after only 24 weeks of gestation? Explain why and show solution. V. A randomly selected baby would be an age of less than x weeks to be one of the bottom 20% in gestational age. What is the value of x? Explain steps and show calculation. Vi. Before what gestational time does 83.4% of gestational time occur? Explain steps and show calculation.

Answer 1

Let X be the gestation Almes for human babies. XN N(402) We want - P(33< X < 36) (zun(0,1)) using standard Normal appronimation, °°( 33-40 <2 = 36-40) = P(-35 42) = P(Z < -2) - P(Z <-3.5) (Since P(25-a) = P(Z <3.5 - Plzsa) = P(Z >a) - 1-(24a) = 0.99977 -0.97725 (from 2-tables) -0.02252 Ans We want P(x<28) =plz <(28-40 = Plz <- 6) =P( 236) 21-P (z<6) <0.00ool V o 1 z score for 9 = -0.67 z score for 82 = +0.67 Aus Now, z = x - M is 1 - 402 -0.67 or 238.66 2 - lower Quartile a +0.67 or n² 41.34 upper guaktile. and n+ 40

- P(x=24) = P (24.5 < x < 33,5). 2P (-7.75 <2 3 - 7:25) - P(22-7.25) -P(2. <-7.15) = P(Z < 7.75) - P(Z < 7:25) 70 so ys it is unsusual