Below is a graph that depicts new born baby weights from data taken from the CDC. We can safely assume they are normally distributed. Baby Birth Weights in the U.S.* average weight: 6 pounds, 9 ounces - 7 pounds, 11 ounces low birth weight: less than 5 pounds, 8 ounces "according to a 2017 CDC report. When we convert the weights to a single unit (ounces) we get: Very low birth weight is less than 54.4 ounces. = Low birth weight between 54.4 ounces and 88 ounces. = Mean birth weight is between 103 and 123 ounces. We will fix the population mean birth rate ( 1 ) to be 114 ounces (or 7 pounds 2 ounces) with population standard deviation { @ ) to be 11.2 ounces (or 0.7 pounds). Use techniques from Chapter 6.2 (e.g. example 3) and the formula given below to answer the following questions. (a) What is the percentile of babies with very low birth weight? (b) What is the percentile range of babies with low birth weight (between 54.4 and 88 ounces)? Your answer should be between x percentile and y percentile. (c) What is the percentile range of babies with mean birth rate (between 103 and 123 ounces)? Your answer should be between x percentile and y percentile. (d) Suppose your friend just had her first baby whose birth weight is 97 ounces (6 pounds 1 ounce), calculate the percentile weight for your friend's new-born baby. (e} What babv weight represents the 67th percentile? (e) What baby weight represents the 67th percentile? (d) Compare your answers with those of others, if there is disagreement on an answer, work it out and post a correction if needed. To compute these values, you will need to use the following formula for (a) - (d) 2 = where o = 11.2 ounces and / = 114 ounces and x is the birth weight in ounces. For (e) we need to do two things. First find the z-score on the standard normal curve that corresponds to the 67th percentile (or cumulative probability equal to 0.67). Using that z-score find the baby weight x using the following formula (we are basically solving for x in the above formula) x = H+ (0 . z) A video where I work (a), (b) and (e) using different values can be viewed below