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Answer :
Final answer:
The probability that a randomly selected newborn hippopotamus weighs between 70 and 90 pounds is 0.5384.
Explanation:
To find the probability that a randomly selected newborn hippopotamus weighs between 70 and 90 pounds, we need to find the area under the normal distribution curve between these two weights. First, we need to convert the weights to z-scores. The z-score formula is given by z = (x - μ) / σ, where x is the given weight, μ is the mean, and σ is the standard deviation. For 70 pounds, z = (70 - 84) / 13 = -1.077. For 90 pounds, z = (90 - 84) / 13 = 0.462.
Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores. The probability of a z-score less than -1.077 is 0.1401, and the probability of a z-score less than 0.462 is 0.6785. To find the probability between these two weights, we subtract the smaller probability from the larger probability: 0.6785 - 0.1401 = 0.5384.
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