Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 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 485 grams. If a 33​-week gestation period baby weighs 2575 grams and a 41​-week gestation period baby weighs 2775 ​grams, find the corresponding​ z-scores. Which baby weighs less relative to the gestation​ period?

The baby born in week __ weighs relatively less since it's z-score, __, is larger/smaller than the z- score of __ for the baby worn in week __.

Answer 1

Let X1 represent weight of babies from 32 to 35 week and X2 represent weights of babies after 40 weeks

z -score = =

Therefore if babies are born during 33 week fall under the catergory 32 - 35 weeks.

Therefore if weight = 2575 then sub x = 2575

= =

z -score =

Therefore if babies are born during 41 weeks fall under the catergory after 40 weeks.

Therefore if weight = 2775 then sub x = 2775

= =

The baby born in week 33 weighs relatively less since it's z-score -0.321, is larger than the z- score of -0.464 for the baby worn in week 41.

This is because z-score helps to calculate the probability of less than x. Since the probability of z-score for 33 is greater than 41 weeks, there are higher chances of 33 week baby to weigh less than 2575 than for 41 week baby.