Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2900
grams and a standard deviation of 700
grams while babies born after a gestation period of 40 weeks have a mean weight of 3400
grams and a standard deviation of 520
grams. If a 33
-week
gestation period baby weighs 3375
grams and a 41
-week
gestation period baby weighs 3875
grams, find the corresponding z-scores. Which baby weighs more
relative to the gestation period?
To find the z-score for a particular weight, we can use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the weight of the baby
- μ is the mean weight for the gestation period
- σ is the standard deviation for the gestation period
For the 33-week gestation period baby:
z = (3375 - 2900) / 700
z ≈ 0.6786
For the 41-week gestation period baby:
z = (3875 - 3400) / 520
z ≈ 0.9183
The z-score compares the weight of the baby to the mean weight for the respective gestation period. A higher z-score indicates being farther above the average weight. Therefore, in this case, the 41-week gestation period baby weighs more relative to the gestation period compared to the 33-week gestation period baby.
Find the corresponding z-scores. Which baby weighs relatively more? Select the correct choice below
A.The baby born in week 41 weighs relatively more since its z-score,--- is larger than the z-score of --- for the baby born in week 33
.
B.The baby born in week 33 weighs relatively more since its z-score, --- is smaller than the z-score of --- for the baby born in week 41
.
C. The baby born in week 33 weighs relatively more since its z-score, --- is larger than the z-score of --- for the baby born in week 41
.
D.The baby born in week 41 weighs relatively more since its z-score,--- is smaller than the z-score of --- for the baby born in week 33
A. The baby born in week 41 weighs relatively more since its z-score, 0.9183, is larger than the z-score of 0.6786 for the baby born in week 33.
Your second answer is correct, but your first answer is incorrect. To determine which baby weighs relatively more
,
compute each baby's z-score. The population z-score can be found using the formula below, where x is the weight, mu
is the appropriate population mean weight, and sigma
is the appropriate population standard deviation.
I apologize for the incorrect first answer. To determine which baby weighs relatively more, we need to compare the z-scores.
To compute each baby's z-score, we will use the formula where z is the z-score, x is the weight of the baby, µ is the mean weight for the gestation period, and σ is the standard deviation for the gestation period.
For the 33-week gestation period baby:
z = (3375 - 2900) / 700
z ≈ 0.6786
For the 41-week gestation period baby:
z = (3875 - 3400) / 520
z ≈ 0.9183
Since the z-score measures how many standard deviations a value is from the mean, we can conclude that the baby with the higher z-score weighs relatively more. Therefore, the correct answer is:
B. The baby born in week 33 weighs relatively more since its z-score, 0.6786, is smaller than the z-score of 0.9183 for the baby born in week 41.
A is the correct answer but the z-score is not 0.6786.
I apologize for the mistake. Let's recalculate the correct z-scores.
For the 33-week gestation period baby:
z = (3375 - 2900) / 700
z ≈ 0.6786
For the 41-week gestation period baby:
z = (3875 - 3400) / 520
z ≈ 0.9183
You are correct, and I apologize for the confusion. The correct answer is:
A. The baby born in week 41 weighs relatively more since its z-score, 0.9183, is larger than the z-score of 0.6786 for the baby born in week 33.
To determine which baby weighs relatively more
,
compute each baby's z-score. The population z-score can be found using the formula below, where x is the weight, mu
is the appropriate population mean weight, and sigma
is the appropriate population standard deviation.
Apologies for the confusion. Let's calculate the correct z-scores using the formula:
For the 33-week gestation period baby:
z = (x - μ) / σ
z = (3375 - 2900) / 700
z ≈ 0.6786
For the 41-week gestation period baby:
z = (x - μ) / σ
z = (3875 - 3400) / 520
z ≈ 0.9183
I apologize once again for the previous incorrect response. The correct answer is:
A. The baby born in week 41 weighs relatively more since its z-score, 0.9183, is larger than the z-score of 0.6786 for the baby born in week 33.
My caculation show the z-score.
z = (3375 - 2900) / 700
z ≈ 0.6786
and
z = (3875 - 3400) / 520
z ≈ 0.9135 You got this calculation wrong.