According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3321 grams and a standard deviation

Mathematics
1

According to the article “Are Babies Normal?” by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3321 grams and a standard deviation of 595 grams.
What is the probability that a randomly selected baby weighs between 3100 grams and 3700 grams? Round your answer to 4 decimal places.

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What is the probability that a randomly selected baby weighs between 3100 grams and 3700 grams?

Answer:
To determine the probability that a randomly selected baby weighs between 3100 grams and 3700 grams, we will use the z-score formula with the given mean and standard deviation.

First, we need to calculate the z-scores for both weights:

  • For 3100 grams:
    z_1 = \frac{3100 - 3321}{595} = -0.3714
  • For 3700 grams:
    z_2 = \frac{3700 - 3321}{595} = 0.6353

Next, we find the area under the standard normal curve between these two z-scores using a standard normal distribution table or a calculator.

By referring to the z-table, the area to the left of -0.3714 is 0.3577 and the area to the left of 0.6353 is 0.7364.

Therefore, the probability that a randomly selected baby weighs between 3100 grams and 3700 grams is the difference between these two areas:
P(-0.3714 < Z < 0.6353) = 0.7364 - 0.3577 = 0.3787

Rounded to four decimal places, the probability is 0.3787.

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