Question

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. 0.76 Birth weights (in pounds) Gestation Period Mean (u) Standard Deviation (6) Under 28 weeks 1.601 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 1.07 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.

QUESTIONS 4-6 PLEASE. MUST INCLUDE:

For questions 4 – 6 you must show the following:

• A sketch of the normal distribution with the appropriate area shaded in.

• The target area as four decimal places.

• The z-score that represents the cutoff point for the area.

• The final answer calculation including a label.

Answer 1

ANSWER! 41 lard largest for a weight gestauon that can be in the bottom 16%. Of babies boon period of 32 to 33 weers. Xn (4:31, (0.97.)?). The required probability is . => PCX <C) = 0.16 » PC wengine C..14.29").-06 > plze set -0.16 → -4.31 - -0.994 0.97 I from the standard Normal table) C = 3.3458 1.4 2:37 3-34 4:31 5.28 6.25 7:22 Cutoff point below which 16% area ties - 3.3458 (5) Smallest weight that can be in the top 4% of the babies bom for a gestation period of 37 to 38 weeks. X~ N(6.92 , 1.0)

P(x>C) = 0.04 => P(Z >4672) 20:04 => P4720 C-6.921- 92 = 1.451 [foom Standard Normal Table] 1.07 → C. 8.7936 3:7 478 $85 672 1.99 9.06 Cutt off point over which 47. area lies - 8.7936 (6) Between two values does the middle 61 y. of the weights lie a gestation penod Of 42 weeks and over: for -0.61 (P) 7:04 7.197 8.16 9.123 9.28 PL7.197 <x<9.123 ): 0.6|| - Thanking you - ***