According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 11.4 pounds and standard deviation 2.8 pounds. What proportion Of babies weigh between 10.3 and 12.5 pounds?

Question

Quizplus · Accepted Answer

To find the proportion of babies with weight between 10.3 and 12.5 pounds, we need to find the area under the normal curve between these two values. We can do this by standardizing the values and using a standard normal table or calculator.

First, we calculate the z-scores for the two weights:

z1 = (10.3 - 11.4)/2.8 = -0.39
z2 = (12.5 - 11.4)/2.8 = 0.39

Next, we look up the area to the left of each z-score using a standard normal table or calculator:

P(Z < -0.39) = 0.349
P(Z < 0.39) = 0.651

Finally, we subtract the area to the left of the lower z-score from the area to the left of the higher z-score to get the proportion between the two values:

P(-0.39 < Z < 0.39) = 0.651 - 0.349 = 0.302

Therefore, the proportion of babies weighing between 10.3 and 12.5 pounds is 0.302 or approximately 0.3035. The best answer choice is B.

According to a Recent Study, the Weight of Male Babies