Question

1. Project A
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 refers to babies who are between 33 and 36 completed weeks of gestation and /or have a birth weight between 1500 and 2500 grams. • Moderate Prematurity refers to babies who are born between 28 and 32 completed weeks of gestation with a birth weight range between 100 and 1500 grams. • Extreme Prematurity refers to babies who are born before 28 completed weeks of gestation or a birth weight less than 1000 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. ii. What is the probability of having a birth with extreme prematurity? 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? 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? vi. Before what gestational time does 83.4% of gestational time occur? b. The birth weight of a baby is approximately normally distributed with an average of 3.4 kg and a standard deviation of 800 grams. i. Calculate the probability of having a birth with moderate prematurity. ii. What is the probability of having birth with extreme prematurity? iii. What is the probability of having a baby weighing at least 6 kg? Do you think it is highly unlikely to have a baby with this weight? explain? iv. A randomly selected baby will weigh more than x kg to be one of the top 5% in weight. What is the value of x? v. Above what weight do 87.7% of the weights occur? vi. Suppose on another planet the baby (may not be human) birth weight X follow the normal distribution. The probability that X exceeds 4 kg is 0.975 and the probability that x exceeds 5 kg is 0.95. Find µ and σ.

Answer 1