Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. If a 34​-week gestation period baby weighs 2975 grams and a 41​-week gestation period baby weighs 3475 ​grams, find the corresponding​ z-scores. Which baby weighs more relative to the gestation​ period?

Answer:The 41 week gestation's period baby has a higher zscore, so he weighs more relative to the gestation​ period.Step-by-step explanation:Normal model problems can be solved by the zscore formula.On a normaly distributed set with mean [tex]\mu[/tex] and standard deviation [tex]sigma[/tex], the z-score of a value X is given by:[tex]Z = \frac{X - \mu}{\sigma}[/tex]The zscore represents how many standard deviations the value of X is above or below the mean [tex]\mu[/tex].In this problem, whichever baby has the higher zscore is the one who weighs more relative to the gestation period.Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams. A 34-week gestation period baby weighs 2975.Here, we have [tex]\mu = 2500, \sigma = 700, X = 2975[/tex].So[tex]Z = \frac{X - \mu}{\sigma}[/tex][tex]Z = \frac{2975 - 2500}{700}[/tex][tex]Z = 0.68[/tex]Babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. A 41-week gestation period baby weighs 3475.Here, we have [tex]\mu = 3000, \sigma = 475, X = 3475[/tex].So[tex]Z = \frac{X - \mu}{\sigma}[/tex][tex]Z = \frac{3475 - 3000}{475}[/tex][tex]Z = 1[/tex]The 41 week gestation's period baby has a higher zscore, so he weighs more relative to the gestation​ period.