Birth weights of babies in the United States can be modeled by a normal distribution with mean of 7.17 pounds and standard deviation 1.21 pounds. Those weighing less than 5.51 pounds are considered to be of low birth weight. What is the probability that a randomly selected baby in the United States will be of low birth weight?
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To find the probability that a randomly selected baby in the United States will be of low birth weight, we need to calculate the area under the normal distribution curve to the left of the cutoff weight of 5.51 pounds. This represents the probability of observing a baby with a birth weight less than 5.51 pounds.
To calculate this probability, we can use the standard normal distribution table or a statistical calculator. Since we are given the mean and standard deviation of the normal distribution, we can convert the cutoff weight into a z-score and then find the corresponding probability.
The z-score is calculated as:
z = (x - μ) / σ
Where x is the cutoff weight, μ is the mean, and σ is the standard deviation. Plugging in the values:
z = (5.51 - 7.17) / 1.21
z ≈ -1.37
Next, we look up the z-score of -1.37 in the standard normal distribution table or use a calculator to find the cumulative probability. For the z-score of -1.37, the cumulative probability is approximately 0.0853.
Therefore, the probability that a randomly selected baby in the United States will be of low birth weight (weighing less than 5.51 pounds) is approximately 0.0853, or 8.53%.