A certain paper suggested that a normal distribution with mean 3,500 grams and standard deviation 530 grams is a reasonable model for birth weights of babies born in Canada. (Round your answers to four decimal places.) What is the probability that a randomly selected Canadian baby weighs either less than 2,000 grams or more than 4,000 grams at birth?
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To calculate the probability that a randomly selected Canadian baby weighs either less than 2,000 grams or more than 4,000 grams at birth, we need to calculate the probability for each case separately and then add them together.
The probability that a randomly selected baby weighs less than 2,000 grams can be calculated by standardizing the value and using the standard normal distribution table:
Z = (2000 - 3500) / 530 ≈ -2.6415
Looking up the corresponding value in the standard normal distribution table, we find that the probability of a Z-score less than -2.6415 is approximately 0.0045.
The probability that a randomly selected baby weighs more than 4,000 grams can be calculated similarly:
Z = (4000 - 3500) / 530 ≈ 0.9434
Using the standard normal distribution table, we find that the probability of a Z-score greater than 0.9434 is approximately 0.1736.
Finally, we add these probabilities together:
P(less than 2,000 grams) or P(more than 4,000 grams) = 0.0045 + 0.1736 ≈ 0.1781
Therefore, the probability that a randomly selected Canadian baby weighs either less than 2,000 grams or more than 4,000 grams at birth is approximately 0.1781.
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