Chapter 5 Elementary Statistics The National Center for Health Statistics keeps records of many health-related aspects of people, including the birth weights of all babies born in the United States. The birth weight of a baby is related to its gestation period (the time between conception and birth). For a given gestation period, the birth weights can be approximated by a normal distribution. The means and standard deviations of the birth weights for gestation periods are shown below. Gestation Period Under 28 weeks 28 to 31 weeks 32 to 33 weeks 34 to 36 weeks 37 to 38 weeks 39 weeks 40 to 41 weeks 42 weeks and over Mean Birth Weight (in pounds) 1.90 4.10 5.08 6.14 7.06 7.48 7.67 7.56 Standard Deviation (in pounds) 1.23 1.88 1.56 1.29 1.09 1.02 1.03 1.10 Information for this case study came from page 260 in Elementary Statistics: Picturing the World, 6th ed. Answer the following questions based on this data. For full credit, you need to include all parts of the directions given below. For questions 1-4: Show conversion of x-value into z-score. Draw a sketch of the normal distribution with the z-score (rounded to two decimal places) located and the appropriate area shaded in. Write the notation of the probability being asked for in terms of z. Find the area by doing the appropriate computation of the final answer, using the normal distribution table, including the appropriate label. 1. What is the probability that a randomly selected baby in the gestation period of under 28 weeks has a weight less than 3.5 pounds? (10 points) 2. For a gestation period of 34 to 36 weeks, what is the probability that a randomly selected baby will weigh between 6.25 and 8.5 pounds at birth? (10 points) 3. For a gestation period of 40 to 41 weeks, what is the probability that a randomly selected baby will weigh more than 9 pounds? (10 points) 4. For a gestation period of 39 weeks, a random sample of 36 babies is drawn from that population. What is the probability that the mean weight for this sample is more than 8 pounds? (10 points) For questions 5-6: Draw a sketch of the normal distribution with the appropriate area shaded in. Indicate what area you need to look up and label it on the graph as 4 decimal places. Indicate the z-score that represents the cutoff point for the area. Calculate your final answer including a label. 5. What is the largest weight that can be in the bottom 16% of babies born for a gestation period of 32 to 33 weeks? (10 points) 6. What is the smallest weight that can be in the top 4% of the babies born for a gestation period of 37 to 38 weeks? (10 points)