Question

Case Study Chapter 5 Elementary Statistics The National Center for Health Statistics keeps records of the birth weights of all babies born in the United States. The birth weights are normally distributed. The different categories for gestation periods are shown below. The gestation period is the time between conception and birth. It has an effect on the birth weight of a baby. A full term baby is born at 40 weeks and preterm babies are born before 37 weeks. The population means and standard deviations of the birth weights for the gestation periods are shown below. Birth weights (in pounds) Gestation Period Mean (u) Standard Deviation (o) Under 28 weeks 1.60 0.76 28 to 31 weeks 3.20 1.02 32 to 33 weeks 4.31 0.97 34 to 36 weeks 5.74 1.13 37 to 38 weeks 6.92 107 39 to 40 weeks 7.60 0.99 41 weeks 8.00 0.99 42 weeks and over 8.16 1.12 Data for this case study came from page 260 in Elementary Statistics: Picturing the World, 7 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 1-3 you must show the following: • The conversion of the x-value into the Z-score (rounded to two decimal places). • A sketch of the normal distribution with the Z-score located and the appropriate area shaded in. • The notation of the probability being asked for in terms of z. • The probability by using the normal distribution table and including the appropriate label on your final answer. 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 39 to 40 weeks, a random sample of 36 babies is drawn from the population. What is the probability that the mean weight for this sample is more than 8 pounds? (10 points)

QUESTIONS 1-3 PLEASE. MUST:

For questions 1 – 3 you must show the following:

• The conversion of the x-value into the z-score (rounded to two decimal places).

• A sketch of the normal distribution with the z-score located and the appropriate area shaded in.

• The notation of the probability being asked for in terms of z.

• The probability by using the normal distribution table and including the appropriate label on your final answer.

Answer 1

SO IPLX <3.5) P(x-u <3.5-4) ) P(Z <3.5-1.6 0.76 Plze 2.5) 2=2.5. NOW PLZ 22.5 = (2.) using table we have - 0 (2-5) = 0.99379 I Thus there is 0.99379 probability that a randomly selected baby in the gestation period of under 28 weeks has a weight less than 3.5 pounds.

Dale Page No. IPL 6.25<x< 8-5) PL 6.25- ll cz< 8.5-l P 6.25- 5.74 <2 < B.as- 5.74 1013 1.13 Pro. 4513 cz< 2.uu25) Zoo 2=0.4513 2=2.4425 P . 4513 2 2 .4425) = P(ZC2.448s) - P(ZZO.4513) = 02 (2.4425) - $z(0.4513) - 0.99266- 0.67364. = 0.31902 Inus there is 0.319 probability that a randomly selected baby in the gestation period of 34 to 36 weeks will lie between 6.25 and 8.5 pounds at birth of u=7.6 we know that X NN/de, 87 Inus for gestation period and o = 0.99 INN [7.69 0.0272)

Udle Page No. PLX 78) Plx-ll > 8-1 Plz> 8- 706 ) C jo.02727 PLZ> 2042s) WITLE 2=2.425 2-0 P(Z > 2.425) = = = 1 - P(Z <2 U25) 1 - 0 z (2.425) 1-0.99245 0.00755 Then there is 0.00755 prababibility that mean weight of 36 babies of gestation beriod 39-40 weeks is more than a pounds.