Question

9. (Normal distribution.) Birth weight of babies delivered at term can be mode a normal distribution with mean p = 200 ounces, and standard deviation o = 20 our Using this model, find: a. The percent of bables delivered at term that weigh between 200 ounces and 216 Ounces b. The percent of bables delivered at term that weigh more than 216 ounces. 10. (Coin Tossing. You shake up 100 pennies in a jar and empty them on a table. Let X denote the number pennies that come up heads. a. Find the mean and standard deviation of X b. What is the approximate) probability that you get somewhere between 48 heads and 52 heads (inclusive) when you perform this experiment? Solve this by calculating P14.5 Y 51.5) for the normal random variable Y that has the same mean and standard deviation as the actual binomial random variable X

Answer 1

dal term can be modeled with 9. (Normal distribution.) Birth weight of babies delivered at term can be mod normal distribution with mean = 200 ounces, and standard deviation = Using this model, find: a. The percent of balles delivered at term that weigh between 200 ounces and 216 ounces. We have z-x-l = 216-200 -0.8 20 from standard noormat table P(2=0.8) = 0.7881 So, f. of bables between 200 sunces to 216 tunced its = (0.7881-0.5) +150 = 28.81% b. The percent of babies delivered at terin that weigh more than 216 ounces. The TS = % of bables that wagh more than 216 ounus (1-0.7881 ) x100 = (0.2119) X100%. = 21.19% Figure: Standard Normal Table z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .5000 4960 4920 4880 4840 4801 4761 4721 4681 4641 0.1 5398 5438 5478 5517 5557 5596 5636 5675 5714 5753 0.2 5793 58325871 59105948 5987 6026 60646103 .6141 0. 3 6179 6217 6255 6293 6331 6368 6406 6443 64806517 0.4 6554 6591 6628 6664 6700 6736 67726808 6844 6879 0.5 6915 6950 6985 70197054 7088 7123 7157 7190 7224 0.6 7257 7291 7324 7357 .7389 7422 7454 74867517 7549 0.7 7580 7611 7642 7673 7704 7734 7764 7794 78237852 0.8 7881 7910 79397967 799580238051 8078 8106 .8133 0.9 81598186 8212 82388264 82898315 8340 83658389 1.0 841384388461 84858508 8531 8554 857785998621